C Challenge

42. Writing Is there an SSSS congruence theorem for parallelograms? Explain.

43. Proof Prove Theorem 6-7. Use the diagram below.

    
    Image Long Description

    Given: A B ↔ ∥ C D ↔ ∥ E F ↔ , A C ¯ ≅ C E ¯ modified eh b with left right arrow above , parallel to , modified c d with left right arrow above , parallel to , modified e f with left right arrow above , comma , eh c bar , approximately equal to , c e bar

    Prove: B D ¯ ≅ D F ¯ b d bar , approximately equal to , d f bar

    (Hint: Draw lines through B and D parallel to A E ↔ modified eh e with left right arrow above and intersecting C D ↔ modified c d with left right arrow above at G and E F ↔ modified e f with left right arrow above at H.)

44. Measurement Explain how to separate a blank card into three strips that are the same height by using lined paper, a straightedge, and Theorem 6-7.

Standardized Test Prep

SAT/ACT

45. PQRS is a parallelogram with m ∠ Q = 4 x m angle , q equals 4 x and m ∠ R = x + 10 . m angle , r equals . x plus 10 . Which statement explains why you can use the equation 4 x + ( x + 10 ) = 180 4 x plus . open x plus 10 close equals 180 to solve for x?

    

    1. The measures of the interior angles of a quadrilateral have a sum of 360.
    2. Opposite sides of a parallelogram are congruent.
    3. Opposite angles of a parallelogram are congruent.
    4. Consecutive angles of a parallelogram are supplementary.

46. In the figure of DEFG below, D E ¯ ∥ G F ¯ . d e bar , parallel to , g f bar , . Which statement must be true?

    

    6. m ∠ D + m ∠ E = 180 m angle , d plus , m angle , e equals 180
    7. m ∠ D + m ∠ G = 180 m angle , d plus , m angle , g equals 180
    8. D E ¯ ≅ G F ¯ d e bar , approximately equal to , g f bar
    9. D G ¯ ≅ E F ¯ d g bar , approximately equal to , e f bar
47. An obtuse triangle has side lengths of 5 cm, 9 cm, and 12 cm. What is the length of the side opposite the obtuse angle?
    1. 5 cm
    2. 9 cm
    3. 12 cm
    4. not enough information

Short Response

48. Find the measure of one exterior angle of a regular hexagon. Explain your method.

Mixed Review

See Lesson 6-1.

Find the sum of the measures of the interior angles of each polygon.

49. decagon
50. 16-gon
51. 25-gon
52. 40-gon

See Lesson 4-6.

53. What additional information do you need to prove Δ A D C ≅ Δ A B C cap delta eh d c approximately equal to cap delta eh b c by the HL Theorem?

    

See Lesson 6-2.

Get Ready! To prepare for Lesson 6-3, do Exercise 54.

54. Two consecutive angles in a parallelogram have measures x + 5 and 4 x − 10 . 4 x minus 10 . Find the measure of the smaller angle.

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