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6.2 Properties of Parallelograms

Goal 1: Use some properties of parallelograms

Use properties of parallelograms in real-life situations

CAS 4, 7, 12

Parallelogram

A parallelogram is a quadrilateral with both pairs of opposite sides parallel and congruent.

P

Q R

S

This is parallelogram: PQRS

QR//PS

SR//PQ

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Theorem 6.2

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

PSQR

P

Q R

S

This is parallelogram: PQRS

SRPQ

Theorem 6.3

If a quadrilateral is a parallelogram, then its opposite angles are congruent.

RP

P

Q R

S

This is parallelogram: PQRS

SQ

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Theorem 6.4

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

180SmPm

P

Q R

S

This is parallelogram: PQRS

180RmQm

Theorem 6.5

If a quadrilateral is a parallelogram, then its diagonals bisect each other.

TSQT

P

Q R

S

This is parallelogram: PQRS

T

RTPT

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Regular Polygons

Any polygons that are both equilateral and equiangular are “regular” polygons

Ex. A Square

Ex. 1 GHJK is a parallelogram. Find the unknown length.

a) JH

b) LH

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Ex. 2 In ABCD, mC =105⁰, Find

the missing angle measures.

Ex. 3 WXYZ is a parallelogram. Find the angle measure of x.

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Ex. 4 UVWX is a parallelogram.

1. If XU=15 and UW=28, find WZ.

2. If m∡VWX=120⁰, find m∡WXU

3. If m∡UVW=55⁰ and m∡VWX 7x-8, find x.