IT Is very informal PPt...../..it gives you many information about this chapter.... Created by PIYUSH BHANDARI

1. INTRODUCTIONINTRODUCTION
*NAME- PIYUSH BHANDARI
*CLASS- 9th
*SECTION- ‘B’
*SCHOOL- KENDRIYA VIDHYALAYA
*SUBJECT- MATHS P.P.T

2. Properties ofProperties of
ParallelogramsParallelograms

3. ParallelogramParallelogram
A parallelogram is named using all four vertices.
You can start from any one vertex, but you must
continue in a clockwise or counterclockwise direction.
For example, the figure above can be either
ABCD or ADCB.
Parallelogram
3
AB CD and BC AD
Definition: A quadrilateral whose opposite sides are parallel.
Symbol: a smaller version
of a parallelogram
Naming:
CB
A D

4. Parallelogram:Parallelogram:
A PARALLELOGRAMARALLELOGRAM ( ) is a
quadrilateral with two pairs of parallel
sides.
For example:
A
B
D
C

5. Parallelogram:Parallelogram:
A PARALLELOGRAMARALLELOGRAM ( ) is a
quadrilateral with two pairs of parallel
sides.
A
B
D
C is a symbol for a
“Parallelogram”
ABCD
AD BC
AB CD

6. Parallelogram:Parallelogram:
Terms to know:
 Opposite sides
A
B
D
C

7. Parallelogram:Parallelogram:
Terms to know:
 Opposite sides AB & DC
A
B
D
C

8. Parallelogram:Parallelogram:
Terms to know:
 Opposite sides AB & DC ; AD & BC
A
B
D
C

9. Parallelogram:Parallelogram:
Terms to know:
 Opposite sides AB & DC ; AD & BC
Opposite angles A & C
AA
B
D
CC

10. Parallelogram:Parallelogram:
A
B
DD
C
Terms to know:
 Opposite sides AB & DC ; AD & BC
Opposite angles A & C ; B & D

11. Parallelogram:Parallelogram:
Terms to know:
 Opposite sides AB & DC ; AD & BC
Opposite angles A & C ; B & D
 Consecutive anglesConsecutive angles A & B;
AA
B
D
C

12. Parallelogram:Parallelogram:
Terms to know:
 Opposite sides AB & DC ; AD & BC
Opposite angles A & C ; B & D
 Consecutive anglesConsecutive angles A & B; B & C
A
BB
D
CC

13. Parallelogram:Parallelogram:
Terms to know:
 Opposite sides AB & DC ; AD & BC
Opposite angles A & C ; B & D
 Consecutive anglesConsecutive angles C & D;
A
B
DD
CC

14. Parallelogram:Parallelogram:
Terms to know:
 Opposite sides AB & DC ; AD & BC
Opposite angles A & C ; B & D
 Consecutive anglesConsecutive angles C & D ; A & D
AA
B
DD
C

15. Parallelogram:Parallelogram:
Terms to know:
 Opposite sides AB & DC ; AD & BC
Opposite angles A & C ; B & D
 Consecutive anglesConsecutive angles C & D ; A & D
 DiagonalsDiagonals AC & BD
A
B
D
C
A
B
D
C

16. When are two trianglesWhen are two triangles
congruent?congruent?
 If two triangles are
congruent, how
many pairs of
congruent parts
can be shown?
 Name these.
CORRESPONDING SIDES
FG ≅ XB
GH ≅ BM
FH ≅ XM
CORRESPONDING ANGLES
∠ F ≅ ∠X
∠ G ≅ ∠B
∠ H ≅ ∠M

17. Properties of ParallelogramProperties of Parallelogram
AB ≅ CD and BC ≅ AD
A C and B D∠ ≅ ∠ ∠ ≅ ∠
180 180
180 180
m A m B and m A m D
m B m C and m C m D
∠ + ∠ = ∠ + ∠ =
∠ + ∠ = ∠ + ∠ =
o o
o o
AP ≅ PC
17
1. Both pairs of opposite sides are congruent.
2. Both pairs of opposite angles are congruent.
3. Consecutive angles are supplementary.
4. Diagonals bisect each other but are not congruent
BP ≅ PDAC and BDP is the midpoint of .
A B
CD
P

18. Opposite sides are parallelOpposite sides are parallel
A
B
D
C
AD BC
AB CD
Properties ofProperties of
ParallelogramsParallelograms

19. Opposite sides are parallel
 Opposite sides are congruentOpposite sides are congruent
A
B
D
C
Properties ofProperties of
ParallelogramsParallelograms

20. Opposite sides are parallel
 Opposite sides are congruent
 Opposite angles are congruentOpposite angles are congruent
A
B
D
C
Properties ofProperties of
ParallelogramsParallelograms

21. AA
BB
D
Opposite sides are parallel
 Opposite sides are congruent
 Opposite angles are congruent
 Consecutive angles are supplementaryConsecutive angles are supplementary
C
Properties ofProperties of
ParallelogramsParallelograms
180BmAm =∠+∠

22. A
B
D
Opposite sides are parallel
 Opposite sides are congruent
 Opposite angles are congruent
 Consecutive angles are supplementaryConsecutive angles are supplementary
C
m A m B 180
m B+m C=180
m C+m D=180
m D+m A=180
∠ + ∠ =
∠ ∠
∠ ∠
∠ ∠
Properties ofProperties of
ParallelogramsParallelograms

23. A
B
D
Opposite sides are parallel
 Opposite sides are congruent
 Opposite angles are congruent
 Consecutive angles are supplementary
 The Diagonals bisect each otherThe Diagonals bisect each other
C
EAE EC
BE ED
≅
≅
Properties ofProperties of
ParallelogramsParallelograms

24. A
B
D
Opposite sides are parallelOpposite sides are parallel
 Opposite sides are congruentOpposite sides are congruent
 Opposite angles are congruentOpposite angles are congruent
 Consecutive angles are supplementaryConsecutive angles are supplementary
 The Diagonals bisect each otherThe Diagonals bisect each other
C
E
Properties ofProperties of
ParallelogramsParallelograms

25. Properties of SpecialProperties of Special
ParallelogramsParallelograms
Prove and apply properties of
rectangles, rhombuses, and squares.
Use properties of rectangles,
rhombuses, and squares to solve
problems.

26. A type of special quadrilateral is a rectangle. A
rectangle is a quadrilateral with four right angles.

27. A rhombus is another special quadrilateral. A
rhombus is a quadrilateral with four congruent
sides.
Like a rectangle, a rhombus is a parallelogram. So you
can apply the properties of parallelograms to
rhombuses.

28. A square is a quadrilateral with four right angles and
four congruent sides. In the exercises, you will show
that a square is a parallelogram, a rectangle, and a
rhombus. So a square has the properties of all three.