Use properties of parallelograms

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6-2 Properties of Parallelograms page 294

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Use properties of parallelograms EXAMPLE 1 Use properties of parallelograms ALGEBRA Find the values of x and y. ABCD is a parallelogram by the definition of a parallelogram. Use Theorem 8.3 to find the value of x. AB = CD Opposite sides of a are . x + 4 = 12 Substitute x + 4 for AB and 12 for CD. x = 8 Subtract 4 from each side. By Theorem 8.4, A C, or m A = m C. So, y ° = 65°. In ABCD, x = 8 and y = 65. ANSWER

GUIDED PRACTICE for Example 1 Find FG and m G. 1. SOLUTION FG = HE x = Opposite sides of a are . x = 8 By Theorem 8.4, E G, or m E = m G. So, G ° = 60°. In FEHG, FG = 8 and m G = 60°. ANSWER

Find the values of x and y. 2. GUIDED PRACTICE for Example 1 Find the values of x and y. 2. SOLUTION JK = ML Opposite sides of a are . 18 = y + 3 Substitute 18 for JK and y + 3 for ML. 15 = y Subtract 3 from each side. By Theorem 8.4, J L, or m J = m L. 2x = 50 Substitute x = 25 Divide 2 from each side. In JKLM, x = 25 and y = 15. ANSWER