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.