28. Proof Prove: If two lines are perpendicular, the product of their slopes is − 1 . negative 1 .
    1. Two nonvertical lines, ℓ 1 script l sub 1  and ℓ 2 , script l sub 2 , comma  intersect as shown below. Find the coordinates of C.
    2. Choose coordinates for D and B. (Hint: Find the relationship between ∠ 1 , ∠ 2 , angle 1 comma angle 2 comma  and ∠ 3 . angle 3 .  Then use congruent triangles.)
    3. Complete the proof that the product of slopes is − 1 . negative 1 .

       
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Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

29. The endpoint of a segment is ( 27 , − 3 ) . open 27 comma negative 3 close .  The midpoint is (3, 4). What is the length of the segment?

30. In the diagram of Δ POR cap delta  below, P O = 16 p o equals 16  and O R = 12 . o r equals 12 .  What is OM?

    

31. ▱ white parallelogram FGHI  has sides with lengths F G = 2 x + 5 , G H = x + 7 , H I = 3 x − 2 , f g equals . 2 x plus 5 comma . g h equals . x plus 7 comma . h i equals . 3 x minus 2 comma  and F I = 2 x . f i equals 2 x .  What is the length of the longer sides of ▱ white parallelogram FGHI ?
32. In Δ ABC , m ∠ A = 55 . cap delta  If m ∠ C m angle c  is twice m ∠ A , m angle eh comma  what is m ∠ B ? m angle b question mark

Mixed Review

See Lesson 6-8.

33. A rectangle ABCD is centered at the origin with A ( − a , b ) . eh open negative eh comma b close .  Without using any new variables, what are the coordinates of point C?

See Lessons 4-2, 4-3, and 4-4.

Explain how you can use SSS, SAS, ASA, or AAS with corresponding parts of congruent triangles to prove each statement true.

34. A B ¯ ≅ C B ¯ eh b bar , approximately equal to , c b bar

    

35. ∠ 1 ≅ ∠ 2 angle , 1 approximately equal to , angle 2

    

36. ∠ K = ∠ M angle , k equals , angle m

    

Get Ready! To prepare for Lesson 7-1, do Exercises 37–40.

See p. 827.

Algebra Solve. Round to the nearest tenth if necessary.

37. x 2 = 144 x squared . equals 144
38. r 2 − 3 = 61 r squared , minus , 3 equals 61
39. y 2 + 10 = 35 y squared , plus , 10 equals 35
40. 7 2 + k 2 = 18 2 7 squared , plus . k squared . equals , 18 squared

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