45. Proof Given: P R ¯ ‖ T Q ¯ , P R ¯ ≅ T Q ¯ ,   P S ¯ ≅ Q S ¯ ,   P Q ¯ p r bar . double vertical bar . t q bar , comma . p r bar , approximately equal to , t q bar , comma , p s bar , approximately equal to , q s bar , comma , p q bar  bisects R T ¯ r t bar

    Prove: Δ P R S ≅ Δ Q T S cap delta p r s approximately equal to cap delta q t s

    

46. Writing The 225 cards in Tracy's sports card collection are rectangles of three different sizes. How could Tracy quickly sort the cards?

C Challenge

Coordinate Geometry The vertices of Δ G H J cap delta g h j  are G ( − 2 , − 1 ) , H ( − 2 , 3 ) , g open negative 2 comma negative 1 close comma h open negative 2 comma 3 close comma  and J ( 1 , 3 ) . j open 1 comma 3 close .

47. Δ K L M ≅ Δ G H J . cap delta k l m approximately equal to cap delta g h j .  Find KL, LM, and KM.
48. If L and M have coordinates L ( 3 , − 3 ) l open 3 comma negative 3 close  and M ( 6 , − 3 ) , m open 6 comma negative 3 close comma  how many pairs of coordinates are possible for K? Find one such pair.
49. 1. How many quadrilaterals (convex and concave) with different shapes or sizes can you make on a three-by-three geoboard? Sketch them. One is shown below.
    2. How many quadrilaterals of each type are there?
    

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

50. Δ H L N ≅ Δ G S T , m ∠ H = 66 , cap delta h l n approximately equal to cap delta g s t comma m angle . h equals 66 comma  and m ∠ S = 42 ? m angle . s equals 42 , question mark  What is m ∠ T ? m angle t question mark
51. The measure of one angle in a triangle is 80. The other two angles are congruent. What is the measure of each?
52. Given A ( 2 , − 6 ) eh open 2 comma negative 6 close  and B ( − 3 , 6 ) , b open negative 3 comma 6 close comma  what is AB?
53. What is the number of feet in the perimeter of a square with side length 7 ft?

Mixed Review

See Lesson 3-8.

Write an equation for the line perpendicular to the given line that contains P.

54. P ( 2 , 7 ) ; y = 3 2 x − 2 p open 2 comma 7 close semicolon , y equals . 3 halves , x , minus 2
55. P ( 1 , 1 ) ; y = 4 x + 3 p open 1 comma 1 close semicolon , y equals . 4 x plus 3

See Lesson 1-7.

Find the distance between the points. If necessary, round to the nearest tenth.

56. A ( 0 , 0 ) , B ( 4 , 3 ) eh open 0 comma 0 close comma b open 4 comma 3 close
57. X ( 11 , 24 ) , Y ( − 7 , 24 ) x open 11 comma 24 close comma y open negative 7 comma 24 close
58. E ( 1 , − 12 ) , F ( 1 , − 2 ) e open 1 comma negative 12 close comma f open 1 comma negative 2 close

Get Ready! To prepare for Lesson 4-2, do Exercises 59–61.

See Lessons 1-4 and 3-2.

What can you conclude from each diagram?

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