8.2 Properties of Parallelograms Geometry http://westm.schoolwires.net/Page/716

Objectives: Use some properties of parallelograms. Use properties of parallelograms in real-lie situations

In this lesson . . . And the rest of the chapter, you will study special quadrilaterals. A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

If a quadrilateral is a parallelogram, then Both pairs of opposite sides are congruent Both pairs of opposite angles are congruent Any pair of consecutive angles are supplementary, and The diagonals bisect each other

Theorems about parallelograms Q R —If a quadrilateral is a parallelogram, then its opposite sides are congruent. ►PQ≅RS and SP≅QR P S

Theorems about parallelograms Q R —If a quadrilateral is a parallelogram, then its opposite angles are congruent. P ≅ R and Q ≅ S P S

Theorems about parallelograms Q R —If a quadrilateral is a parallelogram, then its consecutive angles are supplementary (add up to 180°). mP +mQ = 180°, mQ +mR = 180°, mR + mS = 180°, mS + mP = 180° P S

Theorems about parallelograms Q R —If a quadrilateral is a parallelogram, then its diagonals bisect each other. QM ≅ SM and PM ≅ RM P S

Ex. 1: Using properties of Parallelograms 5 F G FGHJ is a parallelogram. Find the unknown length. Explain your reasoning. JH JK 3 K H J b.

Ex. 2: Using properties of parallelograms Q R PQRS is a parallelogram. Find the angle measure. mR mQ 70° P S

Ex. 3: Using Algebra with Parallelograms Q PQRS is a parallelogram. Find the value of x. mS + mR = 180° 3x + 120 = 180 3x = 60 x = 20 3x° 120° S R Consecutive s of a □ are supplementary. Substitute 3x for mS and 120 for mR. Subtract 120 from each side. Divide each side by 3.

http://www. khanacademy http://www.khanacademy.org/math/geometry/quadrilaterals-and-polygons/v/proof---opposite-sides-of-parallelogram-congruent http://www.khanacademy.org/math/geometry/quadrilaterals-and-polygons/v/proof---diagonals-of-a-parallelogram-bisect-each-other http://www.khanacademy.org/math/geometry/quadrilaterals-and-polygons/v/proof---opposite-angles-of-parallelogram-congruent