32. Think About a Plan The Davis family is planning to drive from San Antonio to Houston. About how far will they have to drive?

    

    • How can you find the distance between the two cities on the map?
    • What proportion can you set up to solve the problem?
33. Reasoning Two polygons have corresponding side lengths that are proportional. Can you conclude that the polygons are similar? Justify your reasoning.
34. Writing Explain why two congruent figures must also be similar. Include scale factor in your explanation.
35. △ J L K white up pointing triangle j l k  and △ R T S white up pointing triangle r t s  are similar. The scale factor of △ J L K white up pointing triangle j l k  to △ R T S white up pointing triangle r t s  is 3 : 1. What is the scale factor of △ R T S white up pointing triangle r t s  to △ J L K ? white up pointing triangle j l k question mark
36. Open-Ended Draw and label two different similar quadrilaterals. Write a similarity statement for each and give the scale factor.

Algebra Find the value of x. Give the scale factor of the polygons.

37. △ W L J ∼ △ Q B V white up pointing triangle w l j , tilde operator white up pointing triangle q b v
38. G K N M ∼ V R P T g k n m tilde operator v r p t

Sports Choose a scale and make a scale drawing of each rectangular playing surface.

39. A soccer field is 110 yd by 60 yd.
40. A volleyball court is 60 ft by 30 ft.
41. A tennis court is 78 ft by 36 ft.
42. A football field is 360 ft by 160 ft.

Determine whether each statement is always, sometimes, or never true.

43. Any two regular pentagons are similar.
44. A hexagon and a triangle are similar.
45. A square and a rhombus are similar.
46. Two similar rectangles are congruent.

47. Architecture The scale drawing below is part of a floor plan for a home. The scale is 1  cm  = 10  ft  . 1 , cm , equals 10 , ft , .  What are the actual dimensions of the family room?

    

C Challenge

48. The lengths of the sides of a triangle are in the extended ratio 2 : 3 : 4. The perimeter of the triangle is 54 in.
    1. The length of the shortest side of a similar triangle is 16 in. What are the lengths of the other two sides of this triangle?
    2. Compare the ratio of the perimeters of the two triangles to their scale factor. What do you notice?

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