46. 1. In the diagram, c = x + y . c equals , x plus , y .  Use Corollary 2 to Theorem 7-3 to write two more equations involving a, b, c, x, and y.
    2. The equations in part (a) form a system of three equations in five variables. Reduce the system to one equation in three variables by eliminating x and y.

    3. State in words what the one resulting equation tells you.

       

47. proof Given: In right △ A B C , B D ¯ ⊥ A C ¯ ,  and  D E ¯ ⊥ B C ¯ . white up pointing triangle eh b c comma , b d bar , up tack , eh c bar , comma , and . d e bar , up tack , b c bar , .
    Prove: A D D C = B E E C fraction eh d , over d c end fraction . equals . fraction b e , over e c end fraction
    

Standardized Test Prep

SAT/ACT

48. The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 5 and 15. What is the length of the altitude?
    1. 3
    2. 5 3 5 square root of 3
    3. 10
    4. 5 5 5 square root of 5
49. A triangle has side lengths 3 in., 4 in., and 6 in. The longest side of a similar triangle is 15 in. What is the length of the shortest side of the similar triangle?
    6. 1 in.
    7. 1.2 in.
    8. 7.5 in.
    9. 10 in.

Short Response

50. Two students disagree about the measures of angles in a kite. They know that two angles measure 124 and 38. But they get different answers for the other two angles. Can they both be correct? Explain.

Mixed Review

See Lesson 7-3.

51. Write a similarity statement for the two triangles. How do you know they are similar?
    

See Lesson 6-2.

Algebra Find the values of x and y in ▱ R S T V . white parallelogram r s t v .

52. R P = 2 x , P T = y + 2 , V P = y , P S = x + 3 r p . equals 2 x comma p t , equals y plus 2 , comma v p equals y comma p s , equals x plus 3
53. R V = 2 x + 3 , V T = 5 x , T S = y + 5 , S R = 4 y − 1 r v equals , 2 x plus 3 , comma v t , equals 5 , x comma t s equals , y plus 5 , comma s r equals , 4 y minus 1

Get Ready! To prepare for Lesson 7-5, do Exercises 54–56.

See Lesson 7-2.

The two triangles in each diagram are similar. Find the value of x in each.

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