Geometry

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Tutors/teachers:

Nikkolas

Tutor and Aerospace Engineer

# Properties of a Parallelogram

#### Lesson Contents

## The Six Main Properties of a Parallelogram

A parallelogram is a quadrilateral with two pairs of parallel sides. The six main properties of a parallelogram are given as:**1.) Opposite sides are parallel.****2.) Opposite sides are congruent.****3.) Opposite angles are congruent.****4.) The diagonals bisect each other.****5.) Adjacent angles are supplementary (meaning their sum is 180°).****6.) If one angle is 90°, then all angles are 90°.**

### Examples of the Properties Being Applied

Let’s go through an example where we apply the 6 properties to parallelogram *ABCD* above.

1.) Opposite sides are parallel.*Side AB* is parallel to *side DC*.*Side AD* is parallel to *side BC*.

2.) Opposite sides are congruent.*Side AB* is equal in length to *side DC*.*Side AD* is equal in length to *side BC*.

3.) Opposite angles are congruent.*∠A* = *∠C**∠B* = *∠D*

4.) The diagonals bisect each other.*Diagonal AC* passes through the center of *diagonal BD*.*Diagonal BD* passes through the center of *diagonal AC*.

5.) Adjacent angles are supplementary (meaning their sum is 180°).*∠A* + *∠B* = 180°*∠B* + *∠C* = 180°*∠C* + *∠D* = 180°*∠D* + *∠A* = 180°

6.) If one angle is 90°, then all angles are 90°.

If *∠A* = 90°, then *∠B*, *∠C*, and *∠D* are also 90°.

Result :

Worksheet 1

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Cheat sheet

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