Assignment

1. CHAPTER-1
Q1. The value of 4 √28 ÷ 3√7 is :
(a) 8/3 (b)16/3 (c)24/3 (d)18/3
Q2. The sum of 2 √5and 3√7 is :
(A) 5√ 7 B) 2√5+3√7 (C)5(√5+ √7) (D) 5√35
Q3. An irrational number between 2 and 2.5 is :
(A) √7 (B) √5 (C) √8 (D) √6.5
Q4. The simplified value of 81) √81 is
(A) 9 (B) 3 (C) 1 (D) 0
Q5. The maximum number of digits in the repeating block of 1/ n where n is a prime number is :
(A) 1 (B) n (C) n+1 (D) n-1
Q6. The decimal expansion of the number √2 is :
(A) a finite decimal (B) 1.414 (C) non – terminating recurring (D) non – terminating, non - recurring
Q7. If x is a positive real number, then √ is :
(A) x 1/24
(B) x1/6
(C) x1/12
(D) x1/20
Q8. The rationalising factor of 1/ √50 is :
(A) 5 √2 (B) √ 2 (C) 50 (D) √ 5
Q9. Among the numbers, 1.101001…., 1.1101001…, 1.011012…., 1.011 , the smallest number is :
(A) 1.101001….. (B) 1.1101001….. (C) 1.011012….. (D) 1. 011
Q10. The quotient obtained when √1500 is divided by 2 √15 is
(A)2 √5 (B) 5 (C)3√ 5 (D) 25
Q11. The number (√2 + √5)2
is :
(A) not a real number (B) rational number (C) an integer (D) irrational number
Q12. The sum of 0.3 and 0. 4 is :
(A) 7/ 10 (B) 7/ 9 (C) 7/ 99 (D) 7/ 11
Q13. The p/q form of 0.777….. where p and q are integers, q ≠0 is :
(A) 77 /90 (B) 7 /10 (C) 7/ 9 (D) 77/ 99
Q14. The product of two irrational numbers is :
(A) Always an irrational number (B) Always an integer
(C) Always a rational number (D) Sometimes rational and sometimes irrational
Q15. The value of
)
)
is :
(A) 4 (B) 1/ 32 (C) 16 (D) 1 /16
Q16. The value of ( 121)1/3
X (11)1/3
is equal to :
(A) 121 (B) 1331 (C) 11 (D) 1/ 11
Q17. If x = √7/ 5 and = p √7 then the value of p is :
(A )5 / √7 (B)7 / 25 (C)25/7 (D) √7/ 5
Q18. If b > 0 and b2
= a then √ is equal to :
(A) -b (B) b (C) √ (D) b2
Q19. (a + √ b) (a - √ b) is equal to :
(A) b2
- a2
(B) a2
- b2
(C) a2
- b (D) b2
– a
Q20. Among the following, the rational number is :
(A) (B)√98 (C) √98 / √2 (D)√14

2. Q21. Value of 81) ! " # is :
(A) 3 (B)1/3 (C) 9 (D)1/9
Q22. Find the two irrational numbers between 0.5 and 0.55.
Q23. Find two rational and irrational numbers between 1/3 and ½
Q24. √147 / √75 is not a rational number as √147 and √75 are not rational. State whether it is true or false.
Justify your answer.
Q25. Show that
A)
$ % &)
% $ &)
÷
%
$"
'
= 1 B)
) $*%)+
!
) %*&)+
!
) &*$)+
!
) $ % &+
= 1
C)
, $ %
+
, % $
= 1 D) ) ./0)
+
.,0
) 0/')
+
0,'
) '/.)
+
',.
= 1
E)
.
. , 0
+
.
. / 0
=
/ 0!)
.! / 0!
F)
√ , √
+
√ , √
+
√ , √1
+
√1, √
+
√ , √2
= 1
G)
$
%"
.!,.0,0!
.
%
&"
0!,0','!
.
&
$"
'!,.',.!
= 1
Q26. Find the value of 729) 5
Q27. Show that 0.235 can be expressed in the form p/q, where p and q are integers and q≠0.
Q28. Taking √2 = 1.414 and π = 3.141, evaluate (1/√2) + π upto three places of decimal.
Q29. Find the decimal expansion of 11
.
Q30. Write in simplest form : a) 8 √45 +2√ 50 - 3√147 b) 12√18+ 6√20 - 6√147 + 3√50
Q31. Evaluate :
a) 4√20 + √245 − √405 b) )√5 + 2√2+ − )√5 − √8+
c) " 8
2
"
!
÷ "
/9
: d) 3√40 − 3√320 − √5
e)
1√9
√ ;, √9
−
9√
√ , 9√
−
√
√ , √
f)
<
" !
=
!>
!?
"
!
= >
"
!
)√ +
g) @5 8 + 27 "
9
A
>
h) B5 8 " +
1
" :C #
i)
= 1!
! = 1
"
?
! ! = 1
= 1 >"
>
!
j)
1 ?
− +
99 !)
k) 125 125 − 125
!
) l)
9 D, 9!<,9!E
9 ,9 D/9!<
m) 5 + 2√6" + 8 − 2√15" n) (4 √3 +3√2) X(4 √3 - 3 √2)
o) (13
+23
+33
)-3/2
Q32. Find the value of a and b, when a + b√15 =
√ , √9
√ / √9
Q33. If a +8√5 =
, √
/ √
+
/ √
, √
, find a and b.
Q34. Write √4 , √3, √6 in ascending order.
Q35. If x =
√9,
√9 /
, y =
√9/
√9 ,
, then find the value of x2
+ y2
+ xy and (x + y)3

3. Q36. If a = 7 - 4√3 then find the value of √ +
√.
Q37. If √2 =1.414, find the value of
√ ,
Q38. Solve : 0. 6 + 0.47
Q39. Find the value of x in the following
a)
.
0
"
/
=
0
.
"
/
b)
9
"
9
" = c) 4) /
− 16) /
= 384
d)
9
" 2
" =
9
"
,
e) 2 4 = 8 32>
Q40. If a = 2 and b = 3 then find the value of ab
+ ba
.
Q41. If x = 3 - 2√2 , find x3
- , x4
- and ( x- )3
Q42. Prove that
, √
+
√ , √9
+
√9, √
is rational.
Q43. If xa
=y, yb
=z and zc
=x then prove that abc = 1.
Q44. If a = 5 + 2 √6 and b = 1/a then what will be the value of a2
+b2
and a3
+b3
.
Q45. Evaluate :
;
√ ;, √ ;, √ ;/ √
, when it is given that √10 = 3.162.
Q46. If x=5 and y=2, find the value of (i)(x y
+ yx
)-1
(ii ()xx
+y y
)-1
Q47. If,
2G* = H9
G
! I
!
/ 1G
9J = )
=
1 2
, prove m-n =2.
Q48. If a =2 +√3 +√5 and b =3 +√3-√ 5 , find (a-2)2
+ (b-3)2
Q49. Simplify : )√ +
!
K ÷ K) !
Q50. Simplify :
, √
+
√ , √9
+ … … … . . +
√ , √2
Q51. If x =
M, N, M/ N
M, N / M/ N
then show that qx2
-px+q=0.
Q52. If √2 =1.414 and √3 = 1.732, then find the value of
9√9/ √
+
9
9√9, √
Q53. If xyz = 1, then show that 1 + + K/ )/
+ 1 + K + O/ )/
+ 1 + O + / )/
= 1
Q54. If x =
√ /
find the value of x3
-3x2
-5x+3.

4. CHAPTER-2
Q1. If - 4 is the zero of the polynomial p(x) = x2
+ 11x + k, then value of k is :
(a) 40 (b) -28 (c) 28 (d) 5
Q2. Maximum number of zeroes in a cubic polynomial are :
(a) 0 (b) 1 (c) 2 (d) 3
Q3. Common factor in quadratic polynomials x2
+ 8x + 15 and x2
+ 3x - 10 is :
(a) x + 3 (b) x + 5 (c) x - 5 (d) x-3
Q4. Constant polynomial is :
(A) 7x (B) 7x2
(C) 7x3
(D) 7
Q5. The factors of a7
+ ab6
are :
(A) a, (a6
+b6
) (B) b, (a6
+b6
) (C) a6
,(a+b) (D)b6
, (a+b)
Q6. The expanded form of + 9
"
9
is :
(A) 9
−
1
− 3 +
9
(B) 9
+
1
+ +
9
(C) 9
+
1
+
!
9
+ 3 (D) 9
+
1
+ 3 −
9
Q7. If x+ y+2= 0 then x3
+y3
+8 equals :
(A) (x +y + 2)3
(B) zero (C) 6xy (D) - 6xy
Q8. The number of real zeroes of the polynomial 4 +x3
+x-3 x2
is :
(A) zero (B) 1 (C) 2 (D) 3
Q9. If p(x)= x3
+ x2
+ √5x + √5 , then the value of p (-√5) is :
(A) -5√5 (B) -4√5 (C) 5+√5 (D) -5+√5
Q10. x + 1/x is :
(A) a polynomial of degree 1 (B) a polynomial of degree 2
(C) a polynomial of degree (-1) (D) not a polynomial
Q11. The remainder when the polynomial p(x) is divided by 2x- 5 is :
(A) p(5) (B) p( -5 ) (C) p " (D) p "
Q12. A polynomial containing two non – zero terms is called a :
(A) zero polynomial (B) quadratic polynomial (C) binomial (D) trinomial
Q13. If 25x2
– y2
= 5 + " 5 − " then the value of y is
(A) 0 (B) 1/ 4 (C) 1/ 2 (D) 1 /√2
Q14. If P
+
P
= −1, (x ≠ y, y ≠ 0) then the value of x3
– y3
is :
(A) - 1 (B) 1 (C) 0 (D) ½
Q15. If a =b+ 3, then a3
– b3
- 9ab is :
(A) 9 (B) 27 (C) 81 (D) 18
Q16. If (2t + 1) is the factor of the polynomial p(t) = 4t3
+ 4t2
– t - 1 then the value of p
/
" is :
(A) - ½ (B)1/2 (C) 1 (D) 0
Q17. The polynomial which does not have (x +1) as a factor in the following is :
(A) x2
- 1 (B) x2
- 4x - 3 (C) 2x2
+ 3x+ 1 (D) x2
+4x+3
Q18. √2 +
√
" is equal to :
(a)4/√2 (B)9/2 (C)4/−√2 (D) 9
Q19. The factors of a3
- 1 are :
(A) (a -1),( a2
+a-1) (B) (a +1),( a2
-a+1) (C) (a +1),( a2
-a-1) D) (a -1),( a2
+a+1)
Q20. The degree of the polynomial p(x)= √3 is :
(A) 3 (B) √3 (C) 1 (D) 0
Q21. Zero of the zero polynomial is :
(A) 1 (B) any real number (C) not defined (D) 0
Q22. The degree of the polynomial (5 -x3
)(x 2
+3x+2) is
(A) 5 (B) 3 (C) 4 (D) 1

5. Q23. The maximum number of zeroes of the polynomial p(y) =my
a
is :
(A) a+1 (B) m (C) m+1 (D) a
Q24. The coefficient of x3
in the expansion of m3
1 − Q
"
9
is
(A) m3
(B) 1/m3
(C) -1 (D) 1
Q25. If (x + 3) is the factor of polynomial x3
+ ax2
+ x + 3 then, the value of a is :
(A) 3 (B) 4 (C) 0 (D) -3
Q26. A cubic polynomial has no. of zeroes :
(A) 2 (B) 1 (C) 3 (D) At least three
Q27. On dividing 5y3
– 2y2
-7y+1 by y, the remainder we get is :
(A)-1 (B) 1 (C) 0 (D) 2
Q28. In the polynomial 1 - √11x, the coefficient of x is :
(A) 1 (B) 11 (C)−√11 (D) √11
Q29. The zeroes of f(x) =x2
+2x are :
(A) 0 , -2 (B) 1 , 2 (C) 0 , 2 (D) 1, -2
Q30. One of the factors of (1+3y)2
+(9y2
-1) is :
(A) (1-3y) (B) (3-y) (C) (3y+1) (D) (y-3)
Q31. If x11
+101 is divided by x+1 , the remainder is :
(A) -1 (B) 102 (C) 0 (D) 100
Q32. Value of 5252
- 4752
is :
(a) 100 (b) 10000 (c) 50000 (d) 100000
Q33. If p =17, the degree of the polynomial p(x)= (p-x)3
+14 is :
(A) 17 (B) 14 (C) 0 (D) 3
Q34. A polynomial in one variable is :
(A) x 2
+ x-2
(B) 2√x+ 7 (C) √2x2
+ 3x (D) x5
+ y4
+ 12
Q35. If a, b, c are all non-zeroes and a+b+c=0, prove
.!
0'
+
0!
.'
+
'!
.0
= 3
Q36. Factorize :
a) 2y3
+ y2
- 2y – 1 b) a6
- b6
c) 27p3
- -
2
p2
+ p
d) (a + b + c)2
- (a - b - c) 2
+ 4b2
- 4c2
e) 2x3
- 9x2
- 11x + 30. f) (2y+ x)2
(y - 2x) + (2x +y)2
(2x - y)
g) a(a + b)2
- 2ab(a + b) h)6x3
- 25x2
+ 32x - 12. i) x 4
- 125xy3
j) x4
y4
- 256z4
k) 9(2a-b)2
-4(2a – b) -13 l) (3x+ 4y)3
- (3x-4y)3
-216x2
y
m) 2√2 a3
+ 16 √2 b3
+ c3
- 12abc n) x3
+ 3x2
y+ 3xy2
+1y3
- 8 o) 3- 12 (a-b)2
p) x4
+ 2x3
y - 2xy3
- y4
q) x2
+3 √2 x + 4 r) (x+2)2
+p2
+2p(x+2)
s) (x2
- 4x) (x2
- 4x – 1) -20
Q37. Using suitable identity find the value of :
1 , 9
1!/ 1 = 9 , 9!
Q38. Using suitable identity evaluate (103)3
or 105 x 97
Q39. Simplify 7x3
+8y3
- (4x+3y) . (16x2
-12xy+9y2
)
Q40. Without calculating the cubes, find the value of (-11)3
+ (8)3
+(3)3
Q41. Examine whether (x + 1) is a factor of 3x2
+ x - 1 ?
Q42. Find the value of k ( k ≠ 0 )if (x-3) is a factor of k2
x3
– kx2
+ 3kx- k.
Q43. If 2x +y = - 5 , prove 8x3
+y3
-30xy+125=0
Q44. Without finding the cubes, factorize (x-2y)3
+(2y-z)3
+(z-x)3
Q45. Using identity find the following product : (2x-y+3z) (x2
+y2
+9z2
+2xy+3yz-6zx)
Q46. If x2
- 3x + 2 is a factor of polynomial x4
- ax3
+ b, then find the values of a and b.
Q47. If a, b, c are real numbers and a2
+b2
+c2
– ab – bc – ca =0 then show that a =b =c.
Q48. Give possible expression for the length and breadth of a rectangle whose area is given by 25a2
-35a+12.
Q49. If x – y =2, and xy =15 find x2
+y2
andx 3
- y3

6. Q50. What must be subtracted from x4
+1so that x4
+1is exactly divisible by x-1. Write the resultant polynomial which is
exactly divisible by x-1.
Q51. Factorise : 9a3
- 27a2
- 100a +300, if 3a +10 is one of its factor.
Q52. If the polynomials p(x)=2x3
+bx2
+3x-5 and q (x)=x3
+x2
-4x+b leave the same remainder when divided by x-2,
prove that b=13/3.
Q53. If x2
+ !
= 23, then find the value of x3
+
Q54. On dividing f(x) =x4
- 2x3
+ 3x2
– ax +b by (x -1) and x+1 we get remainder 5 and 19 respectively. Find the remainder
when f(x) is divided by (x-2).
Q55. Verify x3
- y3
= (x -y) (x2
+xy +y2
). Hence factorise 216 x3
- 125 y3
Q56. Prove that : (a+ b)3
+ (c+b)3
+ (c+a)3
=2(a3
+b3
+c3
- 3abc)
Q57. Express (a- b)3
+ (c-b)3
+ (c-a)3
as a product of its factors
Q58. Expand
.
−
0
+ 1" using identity.
Q59. Find the product of (3x +2y) (3x-2y) (9x2
+4y2
)
Q60. Simplify : + " − " + !" + "
Q61. Simplify
.!/ 0! , 0!/ '! , '!/ .!
./0 , 0/' , '/.
Q62. Factorise : 9x2
+4y2
+z2
-12xy+4yz-6zx.Hence find value when x=1, y=2, and z=-1.
Q63. If x3
- 5x2
– px + 24 = (x - 4) . q(x), then what is the value of p ?
Q64. If a2
+b2
+c2
=280, and ab+bc+ca=9/2, then find the value of (a+b+c) 3
Q65. Find the remainder when the polynomial p(y)=y4
- 3y2
+ 7y - 10 is divided by(y - 2).
Q66. Find the value of x2
+ !
, if x - = √3
Q67. Find the value of C for which the polynomial 2x3
- 7x2
- 3x+ C is exactly divisible by (2x+3). Hence factorize the
polynomial.
Q68. If x and y are two positive real numbers such that x2
+ 4y2
=17 and xy= 2, then find the value of (x +2y).
Q69. If x - a is the factor of 3x2
– mx - na then prove that a =
Q,R
9
.
Q70. If x = 2 and x = 0 are zeroes of the polynomial 2x3
- 5x2
+ px + b, then find the value of p and b.
Q71. If a + b + c = 6 and ab + bc + ca = 11, find the value of a3
+ b3
+ c3
- 3abc
Q72. The polynomial bx3
+ 3x2
– 3 and 2x3
- 5x + b when divided by x - 4 leave the remainders R1 and R2 respectively.
Find the value of b if 2R1 - R2 = 0
Q73. If (x -2) and(x – ½) are factors of px2
+ 5x + r then show that p = r.
Q74. The polynomial p(x) = kx3
+ 9x2
+ 4x - 8 when divided by (x + 3) leaves a remainder 10(1 -k).
Find the value of k.
Q75. If x and y are two positive real numbers such that 8x3
+27y3
= 730 and 2x2
y + 3xy2
= 15 then evaluate : 2x + 3y
Q76. If x+a is a factor of the polynomial x2
+px+q and x2
+mx+n, prove that a =
R/N
Q/M
Q77. Find the value of a3
+b3
+c3
-3abc if a+b+c=5 and a2
+b2
+c2
=29.
Q78. Prove that 2x3
+2y3
+2z3
-6 xyz = (x+y+z)[ (x –y)2
+( y –z)2
+( z- x)2
] .
Hence evaluate : 2(13)3
+2(14)3
+2(15)3
-6X13X14X15
Q79. Find the value of p3
- q3
, if p –q = 10/ 9 and pq= 5/ 3
Q80. If x+y+z= 1, xyz = -1 and xy+yz+zx = -1 , find the value of x3
+y3
+z3
.
Q81. Find the value of (x-a)3
+ (x-b)3
+(x-c)3
-3 (x-a)(x – b)(x-c) if a+b+c =3x
Q82. If "
9
− 9
"
9
− "
9
= 1
 , find x.

7. CHAPTER-6
Q1. If in a triangle ABC, ∠ A+ ∠B = 105,∠B + ∠ C = 120 then ∠ B is :
(a) 65 (b) 80 (c) 35 (d) 45
Q2. A rt. angled isosceles triangle ABC is right angled at A. Then ∠ B is :
(a) 45 (b) 60 (c) 30 (d) 90
Q3. In triangle ABC, BC=AB. If ∠B=70, then ∠A is :
(A) 55 (B) 70 (C) 110 (D) 45
Q4. The angle which is half its supplement is :
(A) 60 (B) 120 (C) 110 (D) 130
Q5. If r, s, t are the sides of a triangle, then which is true ?
(A) r= s+t (B) r=s > t (C) r +s> t (D) t > r+s
Q6. In∆ABC, AB=2.5 cm and BC =6 cm, then the length of AC cannot be :
(A) 3.4 cm (B) 4 cm (C) 3.8 cm (D) 3.6 cm
Q7. If one angle of a triangle is 130, then the angle between the bisectors of the other two angles is :
(A) 50 (B) 65 (C) 145 (D) 155
Q8. In a right angled triangle, one acute angle is double the other, then :
(A) Hypotenuse = double the smallest side (B) Hypotenuse= double the other side
(C) One acute angle is 40 (D) ∆ is an isosceles triangle.
Q9. The measure of an angle which is complement of itself is :
(A) 60 (B) 30 (C) 45 (D) 20
Q10. Which of the following is not a criterion for congruence of triangles :
(A) SAS (B) ASA (C) SSA (D) SSS
Q11. If one angle of a triangle is equal to the sum of the other two angles, then the triangle is :
(A) Obtuse triangle (B) Equilateral triangle (C) Isosceles triangle (D) Right triangle
Q12. If the 3 altitudes of a triangle are equal, then triangle is
(A) right angled triangle (B) Isosceles triangle (C) acute angled triangle (D) Equilateral triangle
Q13. An exterior angle of a triangle is 130 and its two interior opposite angles are equal. Each of the interior
angle is equal to :
(a) 45 (b) 65 (c) 75 (d) 35
Q14. In a right angled triangle, if one acute angle is half the other, then the smallest angle is :
(a) 15 (b) 25 (c) 30 (d) 35
Q15. In ∆ PQR if PQ > QR then :
(A) ∠R >∠ P (B) ∠ P=∠R (C) ∠Q <∠ R (D ∠Q=∠R
Q16. In ∆ABC, if ∠A > ∠ B > ∠ C then :
(A) AB > AC (B) AC < BC (C) AB > BC (D) AC > BC
Q17. If a transversal intersects two parallel line and the interior angles so formed are in the ratio 2 : 3 ,
the greater of the two angles is :
(A) 54 (B) 108 (C) 120 (D) 36
Q18. In ∆ABC if ∠A= 35 and ∠ B =75, then the longest side of the triangle is
(A) AC (B) AB (C) BC (D) AB
Q19. In triangles ABC and PQR, AB=AC, ∠ C=∠P and∠ B=∠Q. The two triangles are :
(A) Isosceles but not congruent (B) Isosceles and congruent
(C) Congruent but not isosceles (D) neither isosceles nor congruent
Q20. In a ∆ ABC, ∠C=65 and∠ B=35 and bisector of∠ BAC meets BC in P, then :
(A) AP > BP > CP (B) BP > AP > CP (C) AP < BP < CP (D) BP < AP < CP
Q21. If in a triangle XYZ, ∠Y >∠ Z and XY= 13 cm, then XZ is
(A) 8 cm (B) 9 cm (C) 13.5 cm (D) 13 cm
Q22. If in two triangles ABC and DEF, AB =DE, BC= EF and AC =DF then ∆ABC ≅ ∆ DEF by congruency rule
(A) RHS (B) SAS (C) SSS (D) ASA
Q23. ∆ABC≅ ∆ FDE in which AB = 6 cm ∠B = 40, ∠ A = 80 and FD = 6 cm, then∠E is :
(A) 50 (B) 80 (C) 40 (D) 60
Q24. In triangles ABC and PRQ, AB=PR and∠ A= ∠P. The two triangles are congruent by SAS axiom if :
(A) BC=QR (B) AC=PQ (C) AC=QR (D) BC=PR
Q25. In the figure, sides PQ and PR are produced and if ∠SQR < ∠TRQ, then :

8. (A) PQ > QR (B) PQ = PR (C) PQ < PR (D) PQ > PR
Q26. In fig, if PS I llll and RQ I llll , Q27. In the given figure, ∠BCD is equal to :
then the value of y is :
(A) 55 (B) 90 (A) 180 (B) ∠ ACB + ∠ ABC
(C) 80 (D) 135 (C) ∠ ACB +∠BAC (D) ∠ BAC +∠ ABC
Q28. In the given figure, the value of x which Q29. In fig. BC||DE. If ∠ABC =∠ CDE = 90
makes POQ a straight line is : and ∠ACB = 30 then the measure of∠ DCE is :
(A) 35 (B) 30 (A) 30 (B) 60
(C) 25 (D) 40 (C) 90 (D) 120
Q30. In the given figure, AB=AC and BD=CD. Q31. In the figure the measure of (a +b +c +d +e +f +g +h +i +j) is :
The ratio ∠ABD : ∠ACD is :
(A) 1 : 1 (B) 1 : 2 (A) 900 (B) 720
(C) 2 : 1 (D) 2 : 3 (C) 540 (D) 360
Q32. If E is a point on side QR of ∆PQR such that Q33. In the figure, if ∠B < ∠A and ∠ D >∠ C, then
PE bisects ∠QPR, then :
(A) QP > QE (B) QE =ER (A) AD >BC (B) AD = BC
(C) QE > QP (D) ER > RP (C) AD < BC (D) AD =2BC
Q34. In figure ∠DOB = 87 and∠ COA =82. If∠ BOA=35 ,then find ∠COB and ∠COD.

9. Q35. In∆ ABC, if ∠A =(2x-5), ∠B =(5x+5), ∠ C= (3x+50), then Find the value of x, ∠A ,∠B and ∠C
Q36. Find the supplement of 4 /3 of right angle.
Q37. If (3x - 58) and (x + 38) are supplementary angles, find x and the angles.
Q38. The degree measure of three angles of a triangle are x ,y, z. If z =
,P
, then find the value of z.
Q39. In an Isosceles triangle ABC, with AB = AC, the bisectors of ∠B and∠ C intersect each other at O. Join A to O.
Show that (i) OB = OC, (ii) AO bisects∠ A.
Q40. In figure, find the measure of x.
Q41. l and m are two parallel lines intersected by Q42. In the figure PR is the angle bisector
another pair of parallel lines ‘p’ and ‘q’ . of∠ APQ. Prove that AB||CD.
Show that ∆ABC ≅ ∆CDA
Q43. In figure if AB||CD||EF and x : y = 3 :2, find z. Q44. In ∆ABC, ∠ B = 45, ∠C = 55, AD bisects∠ A.
Find ∠ADB and ∠ADC.
Q45. Prove that the sum of three altitudes of a triangle is less than the sum of the three sides of the triangle.
Q46. In ∆ABC, if AB is the greatest side, then prove that∠ C > 60.
Q47. ABCD is a square. X and Y are points on the sides AD and BC such that AY=BX. Prove that∠ XAY=∠YBX.
Q48. Prove that the angle between internal bisector of one base angle and the external bisector of the other base
angle of a triangle is equal to one-half of the vertical angle.

10. Q49. If in the figure AB|| CD and CD|| EF. Q50. In the figure, AB|| CD, EF|| DQ.
Then find∠BCE. Determine∠DEF, ∠AED and ∠PDQ.
Q51. In the figure, find x, y and z.
Q52. In figure state which lines are parallel any why ? Q53. If diagonal AC of a quadrilateral ABCD bisects ∠A
and ∠ C, then prove that AB =AD and CD= CB.
Q54. In the figure, PQ > PR. QS and RS are bisectors Q55. In the figure, if O is the mid point of BC and AD,
of ∠Q and ∠R respectively. Show that SQ > SR. then prove that BA and DC are parallel.

11. Q56. If the bisectors of a pair of alternate angles formed by a transversal with two given lines are parallel,
prove that the given lines are parallel.
Q57. D is a point on side BC of ∆ ABC such that AD= AC. Show that AB > AD.
Q58. In ∆ ABC, AB=AC, ∠A=36. The internal bisector of∠ C meets AB at D. Prove that AD=BC.
Q59. If AD is the median of ∆ABC, Prove that AB+AC > 2 AD. or Prove that the sum of two sides of a triangle is
greater than twice the median with respect to the third side.
Q60. Prove that the sum of angles of a triangle is two right angles. If in a right triangle an acute angle is one-
fourth the other, find the acute angle.
Q61. In the Quadrilateral ABCD, prove that BC+AB+DA+ CD > 2AC.
Q62. The sides BC, CA and AB of ∆ABC are produced in order forming exterior angles ∠ACD, ∠ BAE and∠CBF.
Show that ∠CBF+∠BAE+∠ACD =360.
Q63. Prove that “Two triangles are congruent if two angles and the included side of one triangle are equal to
two angles and the included side of other triangle”.
Q64. In the given figure AD is bisector of ∠BAC and Q65. In the given figure ∠x=∠ y and AB=CB.
∠CPD=∠BPD. Prove that ∆CAP ≅ ∆BAP and CP=BP. Prove AE= CD
Q66. In the given figure AD =BC and BD =AC . Q67. In the given figure ∠CAB : ∠BAD = 1 : 2
Prove that ∠ ADB =∠ BCA and ∠DAB = ∠CBA , find all the internal angles of∆ ABC.
Q68. In the given figure D and E are points on the base BC Q69. In the given figure, AP and DP are bisectors of
of a triangle ABC such that AD =AE and ∠BAD= ∠CAE. 2 adjacent angles A and D of quadrilateral ABCD.
Prove that AB=AC and BD=EC. Prove that 2∠APD = ∠B+∠C.
Q70. In the given figure two sides AB and AC and median AM Q71. In the given figure AB =CD and ∠ABC=∠ DCB.
of one triangle ABC are respectively equal to the sides PQ Prove that : ( i) ∆ ABC ≅ ∆ DCB (ii) AC= DB
and QR and median PN of triangle PQR. Show that :
(i) ∆PQN ≅ ∆ABM (ii) ∆ PQR ≅ ∆ABC
Q72. In the given figure, ∠B < ∠A and ∠C <∠ D. Q73. In the given figure∠ ACD =∠ABC and CP
Show that AD < BC bisects∠BCD. Prove that∠ APC= ∠ACP.

12. Q74. In the given figure AC= BC, ∠ DCA = ∠ ECB Q75. In the given figure, l ||m|| n.
and ∠DBC= ∠EAC .Prove that DC = EC and BD = AE. From the figure find the ratio of (x+ y) : (y – x)
Q76. If the bisectors of the base angles of a triangle enclose an angle of 135, prove that the triangle is a right triangle.
Q77. In ∆ ABC, if D is a point on BC. Prove that AB+BC+CA > 2 AD.
Q78. ABC is triangle in which altitudes BE and CF are equal. Then show that :
(i) ∆ABE ≅ ∆ACF and (ii) AB= AC
Q79. LMN is a triangle in which altitudes MP and NQ to sides LN and LM respectively are equal. Show that
∆LMP ≅ ∆LNQ and LM = LN.
Q80. Show that in a right angled triangle, the hypotenuse is the longest side.
Q81. If two parallel lines are intersected by a transversal , then prove that bisectors of the interior angles from a
rectangle.
Q82. In a rhombus ABCD, O is an interior point and OA =OC. Prove D, O, B are collinear.
Q83. ∆ABC and ∆ DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC.
If AD is extended to intersect BC at P, show that :
(i) ∆ACD ≅∆ABD (ii) ∆ACP ≅∆ABP
iii) AP bisects ∠A as well as ∠ D iv) AP is perpendicular bisector of BC.
Q84.If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of interior opposite angles.
Prove it.
Q85. Let OA, OB, OC and OD are rays in the anti clock Q86. In the given figure BAD||EF, ∠AEF=55
wise direction, such that :∠AOB= ∠COD=100, ∠BOC=82, and ∠ ACB =25. Find ∠ ABC.
∠AOD=78.Is it true that AOC and BOD are straight lines?
Justify your answer.
Q87. In the given figure, find a + b. Q88. In the given figure ,prove that x=a+b+c
Q89. In the given figure AOB is a line. OM bisects ∠AOP Q90. In the given figure AB= CF, EF =BD,∠AFE =∠CBD
and ON bisects ∠ BOP. Prove that ∠ MON=90 Prove that (i) ∆CBD ≅ ∆AFE (ii) ∠D =∠E

13. Q91. AD, BE and CF, the altitudes of a triangle ABC are equal. Prove that triangle ABC is an equilateral triangle.
Q92. If a transversal intersects two parallel lines, then the bisectors of any pair of alternate angles are parallel. Prove it.
Q93. Prove that the angle opposite to equal sides of a triangle are equal.
Q94. ABCD is a parallelogram in which diagonals AC and BD intersect at O. Show that
(i) AB+ DA+CD+BC > AC+ BD (ii) 2 (AC+ BD) > AB+ BC+ CD +DA
Q95. In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
Q96. In the given figure, ∠ Q > ∠R. Q97. In the given figure AB = BC, AD = CD
PS is the bisector of ∠ QPR, PM ⊥ QR. Find ∠ MPS Prove that∠ ADE is a right angle and AE = EC
Q98. Two equal pillars AB and CD are standing on Q99. In figure AO I OB. Find ∠ AOC and ∠ BOC.
either side of the road as shown in the figure.
If AF = CE then prove that BE = FD
Q100. In figure a + b = c + d. Q101. Lines PQ and RS intersect each other at O.
Prove that AOC is a straight line. If ∠ POR : ∠ ROQ= 5 :7, find all the angles a, b, c and d.
Q102. In figure ABC is an isosceles triangle with AB = AC. Q103. In the figure AB||CD.
D is a point in the interior of ABC such that ∠CBD = ∠BCD. If ∠ABR= 45 and ∠ROD= 105 ,
Prove that AD bisects ∠ BAC of ∆ ABC. then find ∠ ODC.
Q104. In the given figure, ∠PQR = ∠PRQ, then prove that Q105. In figure OA = OD and ∠ 1= ∠ 2.
∠PQS = ∠PRT. Also find∠ P if ∠PQR=70. Prove that ∆OCB is an isosceles triangle.

14. Q106. In the given figure AB=CD, ∠ABD=∠CDB. Q107. In a rectangle ABCD, E is a point which bisects BC.
Prove that AD=CB. Prove that AE=ED.
Q108. In figure AB = AC, CH = CB and HK||BC. Q109. P and Q are the centres of two intersecting circles.
If ∠ CAX= 137 then find ∠ CHK. Prove that PQ=QR=PR.
Q110. In the given figure, ABC is a triangle. Q111. In the given figure BL ⊥ AC, MC ⊥ LN,
AB= AC, BL ⊥AC and CM⊥ AB. AL=CN and BL =CM.
Show that BL=CM. Also prove AM=AL Prove that ∆NML ≅ ∆ABC
Q112. If two lines intersect each other, then the vertically Q113 .In fig, S is any point in the interior of ∆ PQR .
opposite angles so formed are equal. Prove it. Show that SQ+ SR < PQ +PR
Using above, find the value of x in the given figure :
Q114. In ∆ ABC and ∆PQR, AB=PQ, AC=PR and altitude AM and PN are equal. Show that ∆ABC ≅ ∆ PQR.
Q115. In ∆ABC, AD is the perpendicular bisector of ∠A and D is the mid point of BC. Prove that∆ ABC is an isosceles
triangle.
Q116. Prove that the perimeter of a triangle is greater than sum of its three altitudes.
Q117. If D is the midpoint of the hypotenuse AC of a right triangle ABC, prove that BD= 1 /2 AC.
Q118. Prove that if arms of an angle are respectively parallel to the arms of another angle then the angles are
either equal or supplementary.
Q119. ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal. Show that :
(a)∆ ACF ≅∆ABE (b) AB= AC (c) ∆ ABC is an isosceles triangle.
Q120. In ∆ABC, BD and CD are internal bisector of ∠ B Q121. In the given figure, ∠BCD= ∠ADC and
and ∠C respectively. Prove that 180 +y = 2x. ∠ACB =∠BDA. Prove that (i) AD=BC,(ii) ∠ A =∠ B

15. Q122. If two parallel lines are intersected by a transversal, prove that the bisectors of the interior angles on the
same side of transversal intersect each other at right angles.
Q123. PQR is a triangle in which PQ =PR. S is any point on the side PQ. Through S a line is drawn parallel to QR
intersecting PR at T. Prove that PS= PT.
Q124. In figure AB = AD, ∠ 1= ∠2 and∠ 3= ∠4. Q125. In figure OA =OB, OC = OD and
Prove that AP=AQ. ∠AOB = ∠COD. Prove that AC= BD
Q126. In the figure, AD is a median and BL, CM are Q127. In the given figure D is the mid point of the side
perpendiculars drawn from B and C respectively on BC of a ∆ABC and ∠ABD=50. If AD=BD=CD,
AD and AD produced. Prove that BL =CM. then find the measure of ∠ACD.
Q128. In the figure, if PQ =PS, RQ= RS, then show that Q129. In figure ∠ACB is a right angle and AC= CD
∆ PQR≅ ∆PSR and ∆RQT ≅ ∆RST. Show that the line and CDEF is a parallelogram. If ∠ FEC = 10,
PR is the perpendicular bisector of QS. then calculate ∠ BDE
Q130. In the given figure AD= BD. Prove that BD < AC. Q131. In the given figure, PQ and XY bisects each
other at A. Prove that PX=QY.
Q132. In the given figure AD=AE, BD=EC, prove that AB=AC. Q133. In the given figure AB||CD, ∠FAE=90
, ∠AFE=40,find ∠ECD.
Q134. In the given figure∠ AOC and∠ BOC form a line AB. Q135. In the given figure AE=AD and BD=CE.
If a –b=80, find the values of a and b. Prove that ∆AEB ≅ ∆ ADC

16. Q136. Prove that if one angle of a triangle is equal to the sum of the other two angles, then the triangle is right
angled.
Q137. In an isosceles triangle, prove that the altitude from the vertex bisects the base.
Q138. AD is an altitude of an isosceles triangle ABC in which AB =AC. Show that AD is also the Median of the
triangle.
Q139. In the given figure DE||AF, AD||FG, find x, y Q140. In the given figure AC > AB and D is a point
on AC such that AB= AD. Show that BC > CD.
Q141. In figure, if lines PQ and RS intersect at point T, Q142. In the given figure, AB||CD, ∠AQP=140,
such that ∠PRT =50, ∠RPT =100 and ∠PRD=35. Find∠ QPR and reflex∠ QPR.
∠TSQ=60, find ∠SQT.
Q143. In figure ABCD is a square and EF is parallel Q144. In the given figure, what value of x
to diagonal BD and EM= FM. Prove that will make POQ a straight line :
(i) DF =BE (ii) AM bisects∠BAD.
Q145. In the given figure, a is greater than b, Q146. In figure, AB=AC, AD I BC, BE=DE and CF=DF
by 1/ 6th of a straight angle. Find the values of a and b Prove that : (i)∆ABE ≅ ∆ACF (ii) ∠BAE=∠CAF
Q147. Suppose line segments AB and CD intersect at O in Q148. In figure, AB > AC. Prove that AB > AD.
such a way that AO=OD and OB=OC.
Prove that AC=BD but AC may not be parallel to BD.

17. Q149. In a triangle ABC, AB= AC, BE and CF are respectively, the bisectors of ∠B and ∠C. Prove that ∆EBC≅
∆FCB.
Q150. ABC is a triangle and D is the mid-point of BC. The perpendicular from D to AB and AC are equal. Prove that
the triangle is isosceles.
Q151. In the given figure, if l1|| l2 and l3 || l4, Q152. In the given figure m ||n and p||q. If ∠1=75,
what is y in terms of x ? then Prove that ∠2=∠1 + 1/3 of right angle
Q153. In figure, OA ⊥OD, OC ⊥ OB, OD =OA and Q154 . In figure, AB||DC. If x= 4y / 3 and
OC =OB. Prove that AB= CD. y= 3z / 8 find ∠BCD and ∠ABC.
Q155. In the given figure AB =AC ,BP =PC. Q156. In figure AB ⊥BD, FE⊥ EC, AB=EF, BC= ED.
Prove that ∠ABP =∠ACP Prove that ∆ABD≅ ∆ FEC.
Q157. In the adjoining figure, PQRS is a square Q158. In ∆ABC, side AB is produced to D such that
and SRT an equilateral triangle. BD=BC. If∠ B=60 and ∠A=70 prove that :
Prove that PT =QT and ∠TQR=15. (i) AD > CD (ii) AD > AC
Q159. If two isosceles triangles have a common base, Q160. In the figure LMN is an isosceles ∆ with
prove that the line joining their vertices bisects LM= LN and LP bisects∠ NLQ.
the common base at right angle. Prove that LP|| MN

18. Q161. Side BC of ∆ ABC is produced to D. The bisector of Q162. ABCD is a quadrilateral in which AD =BC
∠ A meets BC at L . Prove that ∠ ABC+∠ ACD=2 ∠ ALC. and ∠DAB = ∠CBA. Prove that BD= AC
Q163. In figure, it is given that RT =TS, ∠ 1=2∠2 and Q164. In the given figure AB||CD and O is the mid-point
∠4=2∠3. Prove that(i) ∆ RBT ≅ ∆SAT (ii) RB =AS of AD. Show that O is also mid-point of BC.
Q165. In the given figure ABCD is a square and M is the Q166. E and F are mid-points of equal sides AB
mid point of AB. PQ ⊥ CM meets AD at P and CB and AC of∆ ABC respectively. Show that BF=CE.
produced at Q. Prove that PA= BQ.
Q167. In the given figure ABCD is a quadrilateral in which Q168. In the given figure ∠3 and ∠ 4 are exterior
∠ABC =73,∠C= 97 and ∠D= 110. If AE|| DC and BE||AD angles of Quadrilateral ABCD at point B and D
and AE intersects BC at F, find the measure of ∠EBF. and∠A = ∠2, ∠C=∠1. Prove that ∠1+∠2 = ∠3+∠4
Q169. In the given figure BA⊥AC and DE⊥EF. Q170. In the given figure AD=BC, AC=BD.
If BA=DE and BF=DC, then prove that AC=EF. Prove that∆ PAB is an isosceles triangle.
Q171. A point O is taken inside an equilateral four sided figure ABCD such that its distances from the angular
points D and B are equal. Show that AO and OC are in one and the same straight line.
Q172. Show that the difference of any two sides of a triangle is less than the third side.

19. Q173. In the given figure, AD and CE are the angle Q174. The sides AB and AC of ∆ABC are produced to point P
bisectors of ∠A and ∠C respectively meeting at O. and Q respectively. If bisectors BO and CO of
If ∠ABC=90, then find∠ AOC. ∠ CBP and ∠BCQ respectively meet at point O
then prove that ∠ BOC= 90 – ½ x.
If x = 70, y = 40 ,then find ∠ BOC.
Q175. In the given figure, AB=AC and AB= AD . Q176. In figure PQ and RS are two mirrors placed parallel
Prove that ∠BCD=90. to each other. An incident ray AB strikes the mirror PQ at B,
or In ∆BDC, if A is a point on BD such that the reflected ray moves along the path BC and strikes the
AB =AD = AC, then prove that ∆BCD is mirror RS at C and again reflects back along CD. a right
angled triangle. Prove that AB||CD.
Q177. AD and BE are the altitudes of an isosceles triangle ABC with AC=BC. Prove that AE=BD.
Q178. In the given figure, RP=RQ and M and N are respectively points on sides QR and PR of ∆PQR, such that QM=PN.
Prove that OP=OQ where O is the point of intersection of PM and QN.
Q179. ∆ ABC is an isosceles triangle with AB = BC. If CE and BF are the medians then prove that ∆ABF ≅ ∆ACE.

20. CHAPTER-4
Q1. Point (- 2, 5) lies in the quadrant :
(a) I (b) II (c) III (d) IV
Q2. If x≠ y, then (x, y) ≠ (y, x), But if x= y, then
(a) (x, y) = (y, x) (b) (x, y) ≠ ( y, x) (c) (x, y ) = (-x, -y) (d) (x, y) = (-x, y)
Q3. If (2 – a + b, b) = (6, 2) then the value of a is :
(A) 2 (B) -2 (C) -4 (D) -6
Q4. If the coordinates of the points are P (2, 3) and Q( 3, 5), then (abscissa of P)- (abscissa of Q) is :
A) 1 (B) -1 (C) -2 (D) -5
Q5. The point M lies in the IV quadrant. The co-ordinates of point M is :
(A) (a, b) (B) (-a, b) (C) (a, - b) (D) (-a, -b)
Q6. If the points A(0 , 2) , B (0, -6) and C(a, 3) lie on y-axis, then the value of a is :
(A) 0 (B) 2 (C) 3 (D) -6
Q7. If x>0 and y<0then the point (x, y) lies in :
(A) I quadrant (B) II quadrant (C) III quadrant (D) IV quadrant
Q8. If a point is on negative side of y-axis at a distance of 3 units from origin then, the co-ordinates of the point are (A)
(0,3) B) (0,-3) (C) (3, 0) (D) (-3 ,0)
Q9. Co-ordinate of a point are(- 2, 3). Its distance from x-axis is :
(A) 2 units (B) -3 units (C) -2 units (D) 3 units
Q10. Ordinate of all points on the x-axis is :
(A) 0 (B) 1 (C) 2 (D) -1
Q11. In a plane, on coordinate axes co – ordinates of points A, O and B are (4, 0), (0, 0), (-3, 0) respectively. The distance
AB is :
(A) 7 units (B) 1 unit (C) 3 units (D) 4 units
Q12. If (x+2, 4)=(5, y-2) then the coordinates (x, y) are :
(A) (7, 12) (B) (6, 3) (C) (3, 6) (D) (2, 1)
Q13. The co – ordinates of every point on the y – axis are of the form :
(A) (y, 0 ) (B) (0, y ) (C) (0, x) (D) (x, 0)
Q14. The point at which the two coordinate axes meet is called :
(A) abscissa (B) ordinate (C) origin (D) quadrant
Q15. A point both of whose coordinates are negative lies in the :
(A) I Quadrant (B) II Quadrant (C) III Quadrant (D) IV Quadrant
Q16. The perpendicular distance of a point P(5, 3) from y-axis is :
(A) 3 units (B) 8 units (C) 5 units (D) 2 units
Q17. By plotting the points O (0, 0) A (1, 0) B(1, 1) C(0 ,1) and joining OA, AB, BC and CO, the figure we obtain is :
(A) Square (B) Rectangle (C) Trapezium (D) Rhombus
Q18. Mirror image of the point (- 1,2) on y - axis is :
(A) (1, 2) (B) ( 1, -2) (C) (2 ,1) (D) (2,-1)
Q19. 3 The point whose ordinate is - 3 and which lies on y-axis is :
(A) (0, -3) (B) (3, -3) (C) (-3, 0) (D) (-3,3)
Q20. A policeman and a thief are equidistant from the jewel box. Upon considering jewel box as origin, the position of
policeman is (0, 5). If the ordinate of the position of thief is zero, then the position of thief is :
(A) (0, - 5) or(-5, 0) (B) (0, 5) or (5, 0) (C) (5, 5) or (0, 0) (D) (5, 0) or (-5,0)
Q21. A point (x, y) lies in the II quadrant. If the signs of x and y are interchanged, then it lies in :
(A) I quadrant (B) IV quadrant (C) II quadrant (D) III quadrant
Q22. The area of the triangle formed by joining the points (4, 0), (0, 0) and (0, 4) is :
(A) 4 sq. Units (B) 12 sq. Units (C) 8 sq. units (D) 16 sq. units
Q23. The point (3, 5) and( -5, 3) lies in the :
(A) Same quadrant (B) IV and II quadrant (C) II and III quadrant (D) II and IV quadrant
Q24. Plot the points A(-2, -2), B(6, 0), C(0, 4) and D (-3, 2) on the graph paper. Draw figure ABCD and write in which
quadrant A and D lie.
Q25. Plot the following points :
Points P Q R S T U
Co-ordination
x -1 0 6 3 -3 6
y 3 3 3 0 -2 -3
What is the difference between the ordinate of points P and Q. Write the points which lies on x-axis and y-axis.

21. Q26. Plot the following points. Join them in order and identify the figure, PQRS thus obtained : P(1, 1), Q(4, 2), R(4, 8),
S(1, 10). Write mirror image of point P on x-axis and y-axis.
Q27. Three vertices of a rectangle ABCD are A(1, 3), B(1, -1) and C(-1, -1). Plot these points on a graph paper and hence
use it to find the coordinates of the 4th vertex D. Also find the area of the rectangle.
Q28. From the given figure, Q29. From the given graph, write :
write the points whose : (i) The coordinates of the points B and F.
(a) ordinate =0 (b) abscissa = 0 (ii) The abscissa of points D and H.
(c) abscissa =-3 (d) ordinate =4 (iii) The ordinate of the points A and C.
(iv) The perpendicular distance of the point G from the x-axis
Q30. Write the coordinates of the vertices of a rectangle whose length and breadth are 4 units and 3 units respectively
has one vertex at the origin, the longer side is on the x-axis and one of the vertices lies in the IVth quadrant. Also find its
area.
Q31. See figure and write the following : Q32. In the given figure, find the co – ordinates of the points
(i) Co-ordinates of point P. A, B, C, D, E and F. Which of the points are mirror images
(ii) Abscissa of point Q. in (i) x - axis (ii) y – axis
(iii) The point identified by the co-ordinates (-4, 5)
(iv) The point identified by the co-ordinates (-3,-6)
Q33. Plot the following points, join them in order and identify the figure thus formed : A (1, 3) B (1, -1) C (7, -1) and D (7,
3). Write the co-ordinate of the point of intersection of the diagonals.
Q34. Plot the points A, B, C and D where :
(i) A, lies on x-axis and is at a distance of 2 units to the left of origin.
(ii) B, lies on y-axis and is at a distance of 4 units above origin.
(iii) C, lies on x and y-axis both.
(iv) D, lies in the second quadrant at a distance of 3 units from x-axis and 2 units from y-axis.

22. CHAPTER-5
Q1. In figure, if AC = BD, then prove that AB = CD. State the postulate used.
Q2. If a point C lies between two points A and B such that AC = BC, then prove that AC= ½ AB.
Q3. In the figure, if A, B and C are three points on a line and B lies between A and C, then prove that AB + BC =AC.
State the Euclid’s axiom/postulate used to prove this.
Q4. Prove that every line segment has one and only one midpoint.
Q5. “Lines are parallel if they do not intersect”, prove the above with suitable diagram.
Q6. In the given figure AC= XD. C is the midpoint of AB and D is the midpoint of XY. Prove AB= XY.
State the Euclid’s axiom used to prove this
Q7. State any two Euclid’s axioms.
Q8. State fifth postulate of Euclid.
Q9. In the given figure, we have ∠1=∠2, ∠3=∠4. Show that∠ ABC=∠DBC. State the Euclid axiom used.
Q10. How many planes can be made to pass through (a) three collinear points (b) three non-collinear points.
Q11. In the given figure, we have AB = AD and AC = AD. Prove that AB = AC. State the Euclid’s axiom to support
this :
Q12. In the given figure AC=DC, CB=CE, Q13. In the given figure, we have AB =BC, BX= BY.
show that AB=DE. Show that AX =CY. State the axiom used.
Write Euclid axiom to support this.

23. CHAPTER-13
Q1. Find the area of a triangle when two sides are 24cm and 10 cm and the perimeter of the triangle is 62 cm.
Q2. A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m, The non – parallel sides are 14 m and
13 m. Find the area of the field.
Q3. Find the area of the triangle
Q4. ∆ ABC is an isosceles triangle with AB = AC. The perimeter of the triangle is 36 cm and AB = 10 cm. What is the area
of the triangle ?
Q5. If the area of an equilateral triangle is 81 √3 cm 2
. Find its perimeter.
Q6. Using Heron’s formula find the area of an equilateral triangle whose perimeter is 24cm. (Take√3 =1.732)
Q7. The length of sides of a right angled triangle are in the ratio 3 : 4 : 5 and perimeter is 144 cm. Find its sides and area.
Q8. The sides of a triangle are x, x + 1, 2x - 1 and its area is x√10 . What is the value of x ?
Q9. Find the area of a triangle whose sides are 16 cm, 14 cm and 10 cm.
Q10. The base of an isosceles triangle is 10 cm and one of its equal sides is 13 cm. Find its area.
Q11. The perimeter of a ∆ is 120 cm and its sides are in the ratio 5 : 12 : 13. Find the area of the triangle.
Q12. In the given figure ABCD is a rhombus with AC = 16 cm and AB = 10 cm. What is the area of the rhombus ABCD.
Q13. A triangle and parallelogram have the same base and same area. If the sides of the triangle are 15 cm, 14 cm and
13 cm and the parallelogram stands on the base 14 cm, find the height of parallelogram.
Q14. Find the area of a rhombus whose perimeter is 200 m and one of the diagonal is 80 m.
Q15. Find the area of a parallelogram whose sides are 13 cm and 14 cm and diagonal is 15 cm.
Q16. Find the area of the quadrilateral, ABCD where AB=7 cm, BC=6 cm, CD=12 cm,DA=15 cm and AC=9 cm.
Q17. A park, in the shape of a quadrilateral ABCD has BC=12 m, AB=9m,∠C= 90,CD =5 m and AD= 8 m. How much area
does it occupy ?
Q18. The sides of a triangular field are 51 m, 37 m and 20 m. Find the number of rose beds that can be prepared in the
field if each rose bed occupies a space of 6 sq. m.
Q19. The sides of a triangle are 5 cm, 12 cm and 13 cm. Find the length of perpendicular from the opposite vertex to the
side whose length is 13 cm.

24. Q20. The sides of a triangular park are in the ratio 3 : 5: 7 and the perimeter is 300 m. Find its area and the length of
perpendicular drawn on the biggest side.
Q21. The sides of a triangle are 120 m, 170m and 250m. Find its area and height of the triangle if base is 250m.
Q22. Black and white coloured triangular sheets are used to make a toy as shown in figure. Find the total area of black
and white colour sheets used for making the toy.
Q23. A rhombus field has green grass for 20 cows to graze. If each side of the rhombus is 52 m and longer diagonal is 96
m, how much area of the grass field will each cow be getting ?
Q24. The sides of a quadrilateral taken in order are 9m , 40 m, 15 m and 28 m respectively. The angle contained by the
first two sides is a right angle. Find its area.
Q25. The unequal side of an isosceles triangle measures 24 cm and its area is 60 cm2
. Find the perimeter of the given
isosceles triangle.
Q26. The sides of a triangular plate are 8 cm, 15 cm and 17 cm. If its weight is 96 gm, find the weight of plate per sq.cm.
Q27. Find the area of an isosceles triangle whose one side is 10 cm greater than its equal side and its perimeter is 100
cm. (Take√ 5 =2.23 )
Q28. The semi-perimeter of a triangle is 132 cm. The product of the difference of semi-perimeter and its respective sides
is 13200 cm3
. Find the area of the triangle.
Q29. The perimeter of an isosceles triangle is 42 cm and its base is 3 /2 times each of the equal sides. Find the length of
each side and area of the triangle.
Q30. The longest side of a right triangle is 90 cm and one of the remaining two sides is 54 cm. Find its area.
Q31. In the given figure ∆ABC is equilateral triangle with side 10 cm and ∆DBC is right angled at ∠ D =90. If BD =6 cm,
find the area of the shaded portion (√3= 1.732 )