Lesson 5.1: Properties of Parallelograms

Geometry

Notes

QUADRILATERALS NOTES

Interior Angles of a Quadrilateral Corollary

The interior angles of a quadrilateral add up to 360°.

EXAMPLE 1 – Solve for x.

PARALLELOGRAM NOTES

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

Below are 4 important theorems regarding the properties of parallelograms:

Parallelogram Opposite Sides Theorem

Opposite sides are congruent in parallelograms.

So set opposite sides equal to each other.

${"font":{"size":"10","color":"#000000","family":"Calibri"},"type":"$","backgroundColor":"#ffffff","aid":null,"id":"2-0","code":"$\\overline {PQ}\\cong \\overline {RS}$","ts":1667935290209,"cs":"p5WiGbPltVcGYcnU4LiL0g==","size":{"width":66,"height":16}}$ and ${"type":"$","code":"$\\overline {QR}\\cong \\overline {PS}$","id":"3-0","backgroundColor":"#ffffff","font":{"family":"Calibri","color":"#000000","size":"10"},"aid":null,"ts":1667935302434,"cs":"58HMQkA5ZuWoKf6vpujEoA==","size":{"width":66,"height":16}}$

Parallelogram Opposite Angles Theorem

Opposite angles are congruent in parallelograms.

So set opposite sides equal to each other.

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Parallelogram Consecutive Angles Theorem

Consecutive angles are supplementary in parallelograms.

BE SURE TO ADD ANGLES IN NEIGHBORING CORNERS AND SET EQUAL TO 180°.

Parallelogram Diagonals Theorem

The diagonals of a parallelogram bisect each other.

So, set the parts of the same diagonal equal to each other.

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EXAMPLE 2 – Find the indicated measure in parallelogram HIJK.

HI =	KH =
KG =	HJ =
mHIJ =	mKJI =
mHIG=	mIKH =

EXAMPLE 3 – Find the value of each variable in the parallelogram.