Properties of Parallelograms

Properties of Parallelograms Students will be able to apply properties of parallelograms

Parallelogram • Any polygon with 4 sides is called a quadrilateral. • Some quadrilaterals have special properties. These special quadrilaterals are given their own names. • A quadrilateral with two pairs of parallel sides is called a parallelogram. This is property 1. • “ ABCD” means “parallelogram ABCD” A B D C Unit G

Property 2 of Parallelograms • If a quadrilateral is a parallelogram, then both pairs of opposite sides are congruent. • If ABCD is a parallelogram, then A B D C Unit G

Property 3 of Parallelograms • If a quadrilateral is a parallelogram, then both pairs of opposite angles are congruent. • If ABCD is a parallelogram, then A B D C Unit G

Property 4 of Parallelograms • If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. • If ABCD is a parallelogram, then A B D C Unit G

Property 5 of Parallelograms • If a quadrilateral is a parallelogram, then its diagonals bisect each other. • If ABCD is a parallelogram, then A B Z D C Unit G

Using these Properties • ABCD is a parallelogram. Find each measure. How do we know this is true? 4x + 2 = 5x – 3 5 = x So AB and DC = 22 4x + 2 A B (5y - 5)º How do we know this is true? (5y - 5) + (8y – 23) = 180 y = 16 So ∠A = 75˚ and ∠D = 105˚ (8y – 23)º D C 5x - 3 Unit G

Check It Out! Example 3 • QRST is a parallelogram. • Find TQ. • Find ∠T. Unit G

Properties of Parallelograms