28. Think About a Plan What are the values of x and y in the parallelogram?

    

    • How are the angles related?
    • Which variable should you solve for first?

Algebra Find the value of a. Then find each side length or angle measure.

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31. Studio Lighting A pantograph is an expandable device shown below. Pantographs are used in the television industry in positioning lighting and other equipment. In the photo, points D, E, F, and G are the vertices of a parallelogram. ▱ D E F G white parallelogram d e f g is one of many parallelograms that change shape as the pantograph extends and retracts.

    

    1. If DE = 2.5 ft, what is FG?
    2. If m ∠ E = 129 , m angle , e equals 129 , comma what is m ∠ G ? m angle g question mark
    3. What happens to m ∠ D m angle d as m ∠ E m angle e increases or decreases? Explain.

32. Proof Prove Theorem 6-4.

    

    Given: ▱ A B C D white parallelogram eh b c d

    Prove: ∠ A angle eh is supplementary to ∠ B . angle b .

    ∠ A angle eh is supplementary to ∠ D . angle d .

Proof Use the diagram below for each proof.

33. Given: ▱ L E N S white parallelogram l e n s and ▱ N G T H white parallelogram n g t h

    Prove: ∠ L ≅ ∠ T angle , l approximately equal to , angle t

34. Given: ▱ L E N S white parallelogram l e n s and ▱ N G T H white parallelogram n g t h

    Prove: L S ¯ ∥ G T ¯ l s bar , parallel to , g t bar

35. Given: ▱ L E N S white parallelogram l e n s and ▱ N G T H white parallelogram n g t h

    Prove: ∠ E angle e is supplementary to ∠ T . angle t .

Proof Use the diagram below for each proof.

36. Given: ▱ R S T W white parallelogram r s t w and ▱ X Y T Z white parallelogram x y t z

    Prove: ∠ R ≅ ∠ X angle , r approximately equal to , angle x

37. Given: ▱ R S T W white parallelogram r s t w and ▱ X Y T Z white parallelogram x y t z

    Prove: X Y ¯ ∥ R S ¯ x y bar , parallel to , r s bar

Find the measures of the numbered angles for each parallelogram.

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41. Algebra The perimeter of ▱ A B C D white parallelogram eh b c d is 92 cm. AD is 7 cm more than twice AB. Find the lengths of all four sides of ▱ A B C D white parallelogram eh b c d .

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