maths

2. To our presentation of
class IX

4. G R O U P

5. 10/19/2016

6. INTRODUCTION
In our daily life we see books, note books , black
boards, walls of the classroom,table,duster,etc….
They are all quadrilaterals. Quadrilaterals are four
sided polygons. We will see more about the
quadrilaterals and special quadrilaterals i.e.
parallelograms ,rectangles, squares etc… in this
presentation.
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7. CONTENT
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8. What is a quadrilateral?
A plane figure bounded by four line
segments AB,BC,CD,DA is called a
quadrilateral.
A
D C
B
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9. A
D C
B
In the above quad ABCD,
•Vertices: Points A,B,C,and D.
•Sides: line segments AB,BC,CD,and DA.
•Angles: <A,<B,<C,<D.(<A+<B+<C+<D=360°)
•Diagonals: line segments AC and BD
•Adjacent sides: AB&BC, BC&CD, CD&DA, DA&AB
•Opposite sides: AB&CD, BC&AD,
•Consecutive angles: <A&<B, <B&<C, <C&<D, <D&<A
•Opposite angles: <A&<C, <B&<D,
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10. Angle sum property of a quadrilateral states that the sum of the angles of a
quadrilateral is 360°
VERIFICATION :-
•Draw a diagonal and divide the quad into two congruent triangles.
•Let ABCD be a quadrilateral and AC be the diagonal
We know that, In DAB,
<ADB+<ABD+<A =180°…….(1) (angle sum property of a triangle)
Similarly ,In BCD,
<DBC+<BDC+<C =180°……..(2) (angle sum property of a triangle)
Adding (1) and (2),we get,
<ADB+<ABD+<A+<DBC+<BDC+<C=180°+180°=360°
Also,
<ADB+<BDC=<D &<ABD+<DBC=<B
So,
<A+<B+<C+<D=360°
i.e., the sum of the angles of a quadrilateral is 360°
A B
D C
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11. Types of quadrilaterals
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12. • Parallelogram:-A quad whose both pairs of
opposite sides are parallel is called a
parallelogram
Here ,ABCD is a parallelogram.
• Rectangle:-A parallelogram in which each
angle is 90°,is called a rectangle.
Here ,PQRS is a rectangle.
C
B
D
A
P Q
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13. • Square:- A rectangle whose all the four sides are
equal is called a square. For a square
ABCD,AB=BC=CD=DA and each angle is 90°
• Rhombus:-A parallelogram whose all sides are
equal is called a rhombus. For a rhombus ABCD,
AB=BC=CD=DA
A
CD
BA
D C
B
8

14. •Trapezium:- a quadrilateral in which one pair of opposite
sides is parallel is called a trapezium. Here ,ABCD is a
trapezium in which AB II DC.
A trapezium is called an isosceles
trapezium if its non parallel sides
are equal
•Kite:- A quadrilateral in which both pairs of adjacent sides are
equal is called a kite. ABCD is a kite in which AB=AD &BC=CD
A
D
C
B
A
B
C
D
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15. Note:-
1. A square ,rectangle and rhombus are all
parallelograms.
2. A square is a rectangle and also a rhombus.
3. A parallelogram is a trapezium.
4. A kite is not a parallelogram.
5. A trapezium is not a parallelogram
6. A rectangle or a rhombus is not a square.
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16. PROPERTIES
OF
QUADRILATERALS
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17. Properties of a PARALLELOGRAM
In the figure, ABCD is a parallelogram in which
AB ll CD and BC ll AD.
on measuring,
i. AB=DC and BC=AD
ii. <A=<C,<B=<D
C
B
D
A
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18. •Property 1: - The diagonal in a parallelogram
divides it into two congruent triangles
•Property 2:- In a parallelogram opposite sides
are equal.
•Property 3:- The opposite angles of a
parallelogram are equal
•Property 4:- The diagonals of a parallelogram
bisect each other.
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19. Properties of a RECTANGLE
• Property 1:-The diagonals of a rectangle are of
equal length.
• Property 2:- A rectangle is parallelogram with
one of its angles a right angle.
• Property 3:-the angle bisectors of a
parallelogram forms a rectangle
P Q
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20. properties of a RHOMBUS
• Property 1:-A rhombus is a parallelogram with
a pair of its consecutive sides equal.
• Property 2:-The diagonals of a rhombus are
perpendicular to each other.
• Property 3:-All the four sides of a rhombus are
equal.
CD
BA
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21. Properties of a SQUARE
• Property 1:- A square is a rectangle with a pair
of consecutive sides equal.
• Property 2:-Each of the angles of a square is a
right angle and each of the four sides is of the
same length
• Property 3:-the diagonals of a square are
equal and perpendicular to each other.
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22. FLASHBACK
• A quadrilateral is a four sided polygon.
• The sum of the angles of a quad is 360°.
• There are many types of quad namely ,
parallelogram,square,kite,rhombus,etc…
• They all have different properties also.
• Here we mainly learnt about
parallelogram,rectangle,rhombus,and,square.
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23. TEAM MEMBERS
• Abhijith.P
• Adwaid
• Amarnath.V
• Ashwin.P
• K.S.Pranav
• K.S.Pranay
• C.M.Jayaram
• Rohith Raj.E
• K.Sooraj
• Sidharth
• Vaishnav 23
•Adithya.K
•Adithya.P.C
•Akshaya Devi
•Anjana.P
•Athira.P.R
•Avani
•Gopika Babu
•Gopika.P
•Gargi.M.V
•Maniprabha
•Megha.N.S
•Rafsa.A.R
• B.Sharanya
•Swathi
•Swetha T

24. 10/19/2016 24

25. The End
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26. 10/19/2016 26

27. Life is good for only two things,
discovering mathematics and teaching mathematics
-Simeon Poisson
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