C Challenge

27. Proof Construction In the figure below, point D is constructed by drawing two arcs. One has center C and radius AB. The other has center B and radius AC. Prove that A M ¯ eh m bar is a median of Δ A B C . cap delta eh b c .

    

28. Probability If two opposite angles of a quadrilateral measure 120 and the measures of the other angles are multiples of 10, what is the probability that the quadrilateral is a parallelogram?

Standardized Test Prep

SAT/ACT

29. From which set of information can you conclude that RSTW is a parallelogram?
    1. R S ¯ ∥ W T ¯ , R S ¯ ≅ S T ¯ r s bar , parallel to , w t bar , comma , r s bar , approximately equal to , s t bar
    2. R S ¯ ∥ W T ¯ , S T ¯ ≅ R W ¯ r s bar , parallel to , w t bar , comma , s t bar , approximately equal to , r w bar
    3. R S ¯ ≅ S T ¯ , R W ¯ ≅ W T ¯ r s bar , approximately equal to , s t bar , comma , r w bar , approximately equal to , w t bar
    4. R Z ¯ ≅ T Z ¯ , S Z ¯ ≅ W Z ¯ r z bar , approximately equal to , t z bar , comma , s z bar , approximately equal to , w z bar

Short Response

30. Write a proof using the diagram.

    Given: Δ N R J ≅ Δ C P T , J N ¯ ∥ C T ¯ cap delta n r j approximately equal to cap delta c p t comma , j n bar , parallel to , c t bar

    Prove: JNTC is a parallelogram.

    

Extended Response

31. Use the figure below.

    
    Image Long Description

    1. Write an equation and solve for x.
    2. Is A F ¯ ∥ D E ¯ ? eh f bar , parallel to , d e bar , question mark Explain.
    3. Is BDEF a parallelogram? Explain.

Mixed Review

See Lesson 6-2.

Algebra Find the value of each variable in each parallelogram.

See Lessons 4-4 and 4-7.

35. Explain how you can use overlapping congruent triangles to prove A C ¯ ≅ B D ¯ . eh c bar , approximately equal to , b d bar , .

    

Get Ready! To prepare for Lesson 6-4, do Exercises 36–44.

See Lessons 5-2 and 6-2.

PACE is a parallelogram and m ∠ P A C = 124 . m angle p eh c , equals 124 , . Complete the following.

36. A C = □ eh c equals white square
37. C E = □ c e equals white square
38. P A = □ p eh equals white square
39. R E = □ r e equals white square
40. C P = □ c p equals white square
41. m ∠ C E P = □ m angle c e p equals white square
42. m ∠ E P A = □ m angle e p eh equals white square
43. m ∠ E C A = □ m angle e c eh equals white square
44. m ∠ A C R = □ m angle eh c r equals white square

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