Bell Ringer 2. 3. 1.

Properties of Parallelograms

Parallelogram Parallelogram – is a quadrilateral with both pairs of opposite sides parallel.

Find Side Lengths of Parallelograms Example 1 Find Side Lengths of Parallelograms FGHJ is a parallelogram. Find JH and FJ. SOLUTION JH = FG Opposite sides of a are congruent. Substitute 5 for FG. = 5 FJ = GH Opposite sides of a are congruent. Substitute 3 for GH. = 3 ANSWER In FGHJ, JH = 5 and FJ = 3. 4

Now You Try  Find Side Lengths of Parallelograms ABCD is a parallelogram. Find AB and AD. 1. ANSWER AB = 9; AD = 8

Find Angle Measures of Parallelograms Example 2 Find Angle Measures of Parallelograms PQRS is a parallelogram. Find the missing angle measures. SOLUTION By Theorem 6.3, the opposite angles of a parallelogram are congruent, so mR = mP = 70°. 1. 2. By Theorem 6.4, the consecutive angles of a parallelogram are supplementary. Consecutive angles of a are supplementary. mQ + mP = 180° Substitute 70° for mP. mQ + 70° = 180° Subtract 70° from each side. mQ = 110° 6

Example 2 Find Angle Measures of Parallelograms By Theorem 6.3, the opposite angles of a parallelogram are congruent, so mS = mQ = 110°. 3. ANSWER The measure of R is 70°, the measure of Q is 110°, and the measure of S is 110°. 7

Now You Try  mB = 120° mC = 60° mD = 120° ANSWER mA = 75° Find Angle Measures of Parallelograms ABCD is a parallelogram. Find the missing angle measures. 2. ANSWER mB = 120° mC = 60° mD = 120° ANSWER mA = 75° mB = 105° mC = 75° 3.

Find Segment Lengths Diagonals of a bisect each other. Example 3 Find Segment Lengths TUVW is a parallelogram. Find TX. SOLUTION TX = XV Diagonals of a bisect each other. Substitute 3 for XV. = 3 9

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