## Properties of a Parallelogram Lesson

### 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:

**Opposite sides are parallel.****Opposite sides are congruent.****Opposite angles are congruent.****The diagonals bisect each other.****Adjacent angles are supplementary (meaning their sum is 180°).****If one angle is 90°, then all angles are 90°.**

INTRODUCING

#### Examples of the Properties Being Applied

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

- Opposite sides are parallel.
*Side AB*is parallel to*side DC*.*Side AD*is parallel to*side BC*. - Opposite sides are congruent.
*Side AB*is equal in length to*side DC*.*Side AD*is equal in length to*side BC*. - Opposite angles are congruent.
*∠A*=*∠C**∠B*=*∠D* - The diagonals bisect each other.
*Diagonal AC*passes through the center of*diagonal BD*.*Diagonal BD*passes through the center of*diagonal AC*. - Adjacent angles are supplementary (meaning their sum is 180°).
*∠A*+*∠B*= 180°*∠B*+*∠C*= 180°*∠C*+*∠D*= 180°*∠D*+*∠A*= 180° - If one angle is 90°, then all angles are 90°.

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