This document discusses the properties of parallelograms. It defines key terms like congruent, bisect, consecutive angles, supplementary angles, and parallel. It then lists six properties of parallelograms: 1) A diagonal divides a parallelogram into two congruent triangles, 2) Opposite sides are congruent, 3) Opposite angles are congruent, 4) Consecutive angles are supplementary, 5) If one angle is right, all angles are right, and 6) The diagonals bisect each other. An example problem demonstrates applying these properties to show that a given quadrilateral is a parallelogram. In closing, it wishes the reader a nice day.

1. Hello everyone!
Learning is FUN.

2. CONDITIONS
THAT GUARANTEE THAT A
QUADRILATERAL
IS A
PARALLELOGRAM

3. Terms
to
Remember

4.  Congruent: Having the same size or
shape, and denoted by the symbol ≅.
 Bisect: To divide into two congruent parts.
 Consecutive Angles: Two angles are
consecutive angles if one of the rays of the
two angles are collinear.

5.  Supplementary Angles: Two angles
whose measures have the sum of
180ᴼ.
 Parallel: Lines in the same plane that
do not intersect. It is denoted by the
symbol ║.

6. PARALLELOGRAM
 It is a quadrilateral with
opposite sides parallel.
 The figure at the right is a
parallelogram with MA║HT
and MH║AT. It is named as
M A
H T
MATH

7. PROPERTIES
OF
PARALELLOGRAMS

8. 1. A diagonal of a parallelogram divides it into two congruent triangles.
M A
H T
 Using the diagonal MT from the parallelogram MATH, it shows that
∆MAT ≅ ∆THM.

9. 2. Opposite sides of a parallelogram are congruent.
M A
H T
 Using the diagonal MT from parallelogram MATH, we have
∆MAT ≅ ∆THM. By CPCTC, we obtain MA ≅ HT and MH ≅ AT.

10. 3. Opposite angles of a parallelogram are congruent.
L O
E V
1
2
M A
H T
3
4
 Using the diagonal LV from parallelogram LOVE and diagonal AH from
parallelogram MATH, we have ∆LOV ≅ ∆VEL and ∆HMA ≅ ∆ATH. By
CPCTC, we have ∠1 ≅ ∠2 and ∠3 ≅ ∠4.

11. 4. Consecutive angles of a parallelogram are supplementary.
M A
H T
 MA║HT and MH is a transversal. We know
that interior angles on the same side of a
transversal are supplementary. Therefore,
∠M + ∠H = 180ᴼ.
 Similarly, ∠A + ∠T = 180ᴼ ,
∠M + ∠A = 180ᴼ, and
∠H + ∠T = 180ᴼ.

12. 5. If one angle in a parallelogram is right, then all angles are right.
C A
R
E
 If ∠C = 90ᴼ, then ∠R = 90ᴼ since ∠C and ∠R
are opposite angles then they are congruent.
 If ∠C = 90ᴼ, then ∠A = 90ᴼ since ∠C and ∠A
are consecutive angles and are supplementary.
 If ∠A = 90ᴼ, then ∠E = 90ᴼ since ∠A and ∠E
are opposite angles.
 Therefore, all the angles of the parallelogram
are 90ᴼ.
 If all the angles of a parallelogram
is 90ᴼ, then it is a rectangle.
Note:
The sum of the interior angles of
a quadrilateral is 360ᴼ.

13. 6. The diagonals of a parallelogram bisect each other.
MT and AH meets at point
C. If C is the midpoint of
MT and AH, then MC ≅ TC
and HC ≅ AC. Therefore,
MT and AH bisects each
other.
M A
H T
C

14. EXAMPLES

15. Given BLUE is a quadrilateral. Complete each statement, then name the
definition or property that supports the answer so that BLUE is a
parallelogram.
B L
E U
R
 BL ║_______
 ∆BLE ≅ _____
 RE = _____
 LU = _____
 m∠UEB + m∠EBL = _______
 m∠LUE = _______

16. B L
E U
R
Definition of parallelogram.
EU
BL ║ _____

17. B L
E U
R
A diagonal of parallelogram divides it into two
congruent triangles.
∆UEL
∆BLE ≅ _______

18. B L
E U
R
The diagonals of a parallelogram bisect each other.
RL
RE = _____

19. B L
E U
R
Opposite sides of a parallelogram are congruent.
BE
LU = _____

20. B L
E U
R
Consecutive angles of a parallelogram are
supplementary.
180ᴼ
m∠UEB + m∠EBL = _______

21. B L
E U
R
Opposite angles of a parallelogram are congruent.
∠EBL
∠LUE = _____

22. THANK
YOU
HAVE A NICE
DAY!
I
MATh