31. Proof In Theorem 6-17, replace “a pair of opposite angles” with “one angle.” Write a paragraph that proves this new statement to be true, or give a counterexample to prove it to be false.

Standardized Test Prep

SAT/ACT

32. Each diagonal of a quadrilateral bisects a pair of opposite angles of the quadrilateral. What is the most precise name for the quadrilateral?
    1. parallelogram
    2. rhombus
    3. rectangle
    4. not enough information
33. Given a triangle with side lengths 7 and 11, which value could NOT be the length of the third side of the triangle?
    6. 13
    7. 7
    8. 5
    9. 2
34. What is the sum of the measures of the exterior angles in a pentagon?
    1. 180
    2. 360
    3. 540
    4. 108

Short Response

35. The midpoint of P Q ¯ p q bar is ( − 1 , negative 1 comma 4). One endpoint is P ( − 7 , 10 ) . p open negative 7 comma 10 close . What are the coordinates of endpoint Q? Explain your work.

Mixed Review

See Lesson 6-4.

Find the measures of the numbered angles in each rhombus.

See Lesson 2-3.

Write the two conditionals as a biconditional.

39. If a parallelogram is a rhombus, then its diagonals are perpendicular.

    If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

40. If a parallelogram is a rectangle, then its diagonals are congruent.

    If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Get Ready! To prepare for Lesson 6-6, do Exercises 41–43.

See Lesson 1-3.

Algebra Find the values of the variables. Then find the lengths of the sides.

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