B Apply

17. Writing Combine each of Theorems 6-3, 6-4, 6-5, and 6-6 with its converse from this lesson into biconditional statements.

18. Developing Proof Complete this two-column proof of Theorem 6-10.

    Given: ∠ A ≅ ∠ C , angle , eh approximately equal to , angle c comma ∠ B ≅ ∠ D angle , b approximately equal to , angle d

    Prove: ABCD is a parallelogram.

    

    Statements	Reasons
    1) x + y + x + y = 360	1) The sum of the measures of the angles of a quadrilateral is 360.
    2) 2(x+ y) = 360	2) a. _ ? modified under bar with question mark above
    3) x + y = 180	3) b. _ ? modified under bar with question mark above
    4) ∠ A angle eh and ∠ B angle b are supplementary. ∠ A angle eh and ∠ D angle d are supplementary.	4) Definition of supplementary
    5) c. _ ? ∥ _ ? , _ ? ∥ _ ? modified under bar with question mark above , parallel to , modified under bar with question mark above , comma , modified under bar with question mark above , parallel to , modified under bar with question mark above	5) d. _ ? modified under bar with question mark above
    6) ABCD is a parallelogram.	6) e. _ ? modified under bar with question mark above

19. Proof Think About a Plan Prove Theorem 6-12.

    Given: B C ¯ ∥ D A ¯ , B C ¯ ≅ D A ¯ b c bar , parallel to , d eh bar , comma , b c bar , approximately equal to , d eh bar

    Prove: ABCD is a parallelogram.

    

    • How can drawing diagonals help you?
    • How can you use triangles in this proof?

20. Proof Prove Theorem 6-8.

    Given: A B ¯ ≅ C D ¯ , B C ¯ ≅ D A ¯ eh b bar , approximately equal to , c d bar , comma , b c bar , approximately equal to , d eh bar

    Prove: ABCD is a parallelogram.

    

21. Proof Prove Theorem 6-9.

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

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

    Prove: ABCD is a parallelogram.

    

Algebra For what values of the variables must ABCD be a parallelogram?

22. 
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25. Proof Given: Δ T R S ≅ Δ R T W cap delta t r s approximately equal to cap delta r t w

    Prove: RSTW is a parallelogram.

    

26. Open-Ended Sketch two noncongruent parallelograms ABCD and EFGH such that A C ¯ ≅ E G ¯ eh c bar , approximately equal to , e g bar and B D ¯ ≅ F H ¯ . b d bar , approximately equal to , f h bar , .

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