Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Algebra Find the value of x in each parallelogram.

See Problem 2.

13. Developing Proof Complete this two-column proof of Theorem 6-6.

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

    Prove: A C ¯ eh c bar and B D ¯ b d bar bisect each other at E.

    

    Statements	Reasons
    1) ABCD is a parallelogram.	1) Given
    2) A B ¯ ∥ D C ¯ eh b bar , parallel to , d c bar	2) a. _ ? modified under bar with question mark above
    3) ∠ 1 ≅ ∠ 4 ; ∠ 2 ≅ ∠ 3 angle , 1 approximately equal to , angle 4 semicolon angle , 2 approximately equal to , angle 3	3) b. _ ? modified under bar with question mark above
    4) A B ¯ ∥ D C ¯ eh b bar , parallel to , d c bar	4) c. _ ? modified under bar with question mark above
    5) d. _ ? modified under bar with question mark above	5) ASA
    6) A E ¯ ≅ C E ¯ ; B E ¯ ≅ D E ¯ eh e bar , approximately equal to , c e bar , semicolon , b e bar , approximately equal to , d e bar	6) e. _ ? modified under bar with question mark above
    7) f. _ ? modified under bar with question mark above	7) Definition of bisector

See Problem 3.

Algebra Find the values of x and y in ▱ P Q R S white parallelogram p q r s .

14. PT = 2x, TR =y + 4, QT = x + 2, TS = y
15. PT = x + 2, TR = y, QT = 2x, TS =y + 3
16. PT = y, TR =x + 3, QT = 2y, T S = 3 x − 1 t s equals 3 x minus 1

See Problem 4.

In the figure, PQ = QR = RS. Find each length.

Image Long Description

17. ZU
18. XZ
19. TU
20. XV
21. YX
22. YV
23. WX
24. WV

B Apply

Algebra Find the value(s) of the variable(s) in each parallelogram.

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