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Warm Up Find the value of each variable.

Warm Up Find the value of each variable. A quadrilateral with two pairs of parallel sides is a parallelogram . To write the name of a parallelogram, you use the symbol. In CDEF , DE = 74 mm, DG = 31 mm, and m  FCD = 42° . Find CF. Example 1A: Properties of Parallelograms.

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Warm Up Find the value of each variable.

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  1. Warm Up Find the value of each variable.

  2. A quadrilateral with two pairs of parallel sides is a parallelogram. To write the name of a parallelogram, you use the symbol .

  3. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF. Example 1A: Properties of Parallelograms CF = DE CF = 74 mm

  4. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find mEFC. cons. s supp. Example 1B: Properties of Parallelograms mEFC + mFCD = 180° mEFC + 42= 180 Substitute 42 for mFCD. mEFC = 138° Subtract 42 from both sides.

  5. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find DF. diags. bisect each other. Example 1C: Properties of Parallelograms DF = 2DG DF = 2(31) Substitute 31 for DG. DF = 62 Simplify.

  6. opp. s  Example 2A: Using Properties of Parallelograms to Find Measures WXYZ is a parallelogram. Find YZ. YZ = XW Def. of  segs. 8a – 4 = 6a + 10 Substitute the given values. Subtract 6a from both sides and add 4 to both sides. 2a = 14 a = 7 Divide both sides by 2. YZ = 8a – 4 = 8(7) – 4 = 52

  7. cons. s supp. Example 2B: Using Properties of Parallelograms to Find Measures WXYZ is a parallelogram. Find mZ. mZ + mW = 180° (9b + 2)+ (18b –11) = 180 Substitute the given values. Combine like terms. 27b – 9 = 180 27b = 189 b = 7 Divide by 27. mZ = (9b + 2)° = [9(7) + 2]° = 65°

  8. 3. diags. bisect each other 2. opp. sides  Example 4A: Using Properties of Parallelograms in a Proof Write a two-column proof. Given: ABCD is a parallelogram. Prove:∆AEB∆CED 1. ABCD is a parallelogram 1. Given 4. SSS Steps 2, 3

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