properties of parallelogram...created by piyush bhandari
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INTRODUCTIONINTRODUCTION
*NAME- PIYUSH BHANDARI*CLASS- 9th
*SECTION- ‘B’*SCHOOL- KENDRIYA VIDHYALAYA
*SUBJECT- MATHS P.P.T
Properties of Properties of
ParallelogramsParallelograms
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.
Parallelogram3
AB CD and BC AD
Definition: A quadrilateral whose opposite sides are parallel.
Symbol: a smaller versionof a parallelogram
Naming:
CB
A D
Parallelogram:Parallelogram:
A PARALLELOGRAMARALLELOGRAM ( ) is a quadrilateral with two pairs of parallel sides.
For example:A
B
D
C
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 BCAB CD
Parallelogram:Parallelogram:
Terms to know: Opposite sides
A
B
D
C
Parallelogram:Parallelogram:
Terms to know: Opposite sides AB & DC
A
B
D
C
Parallelogram:Parallelogram:
Terms to know: Opposite sides AB & DC ; AD &
BC
A
B
D
C
Parallelogram:Parallelogram:
Terms to know: Opposite sides AB & DC ; AD & BCOpposite angles A & C
AA
B
D
CC
Parallelogram:Parallelogram:
A
B
DD
C
Terms to know: Opposite sides AB & DC ; AD & BCOpposite angles A & C ;
B & D
Parallelogram:Parallelogram:
Terms to know:Opposite sides AB & DC ; AD & BCOpposite angles A & C ;
B & DConsecutive anglesConsecutive angles A & B;
AA
B
D
C
Parallelogram:Parallelogram:
Terms to know:Opposite sides AB & DC ; AD & BCOpposite angles A & C ; B
& DConsecutive anglesConsecutive angles A & B; B & C
A
BB
D
CC
Parallelogram:Parallelogram:
Terms to know:Opposite sides AB & DC ; AD & BCOpposite angles A & C ;
B & DConsecutive anglesConsecutive angles C & D;
A
B
DD
CC
Parallelogram:Parallelogram:
Terms to know:Opposite sides AB & DC ; AD & BCOpposite angles A & C ; B
& DConsecutive anglesConsecutive angles C & D ; A & D
AA
B
DD
C
Parallelogram:Parallelogram:
Terms to know:Opposite sides AB & DC ; AD & BCOpposite angles A & C ; B &
DConsecutive anglesConsecutive angles C & D ; A & DDiagonalsDiagonals AC & BD
A
B
D
C
A
B
D
C
When are two When are two triangles congruent?triangles congruent?
If two triangles are congruent, how many pairs of congruent parts can be shown?
Name these.
CORRESPONDING SIDESFG XB GH BMFH XM
CORRESPONDING ANGLES F X G B H M
Properties of ParallelogramProperties of Parallelogram
ABCD 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
AP PC17
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
BPPDAC and BDP is the midpoint of .
A B
CDP
Opposite sides are parallelOpposite sides are parallel
A
B
D
C
AD BC
AB CD
Properties of Properties of
ParallelogramsParallelograms
Opposite sides are parallel Opposite sides are congruentOpposite sides are congruent
A
B
D
C
Properties of Properties of
ParallelogramsParallelograms
Opposite sides are parallel Opposite sides are congruent Opposite angles are congruentOpposite angles are congruent
A
B
D
C
Properties of Properties of
ParallelogramsParallelograms
AA
BB
D
Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are Consecutive angles are supplementarysupplementary
C
Properties of Properties of
ParallelogramsParallelograms
180BmAm
A
B
D
Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are Consecutive angles are supplementarysupplementary
C
m A m B 180m B+m C=180m C+m D=180m D+m A=180
Properties of Properties of
ParallelogramsParallelograms
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 ECBE ED
Properties of Properties of
ParallelogramsParallelograms
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 of Properties of
ParallelogramsParallelograms
Properties of Special Properties of Special ParallelogramsParallelograms
Prove and apply properties of rectangles, rhombuses, and squares.
Use properties of rectangles, rhombuses, and squares to solve
problems.
A type of special quadrilateral is a rectangle. A rectangle is a quadrilateral with four right angles.
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.
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.