Name Class Date. Determining Polygon Similarity
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1 Name lass ate atios in Similar Polygons oing eeper ssential question: How can you use ratios of corresponding side lengths to solve problems involving similar polygons? Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional. The similarity ratio of two similar figures is the ratio of any side length in the first figure to the corresponding side length in the second figure. To prove that two figures with corresponding angles congruent are similar, show that corresponding side lengths are proportional PP FO -ST.1.2 XMPL etermining Polygon Similarity orresponding angles in each pair are congruent. Use ratios of corresponding side lengths to tell whether the figures are similar. If so, name the similarity ratio. rectangle to rectangle WX parallelogram KLMN to parallelogram PQS 1 1 X W etermine the ratios of corresponding lengths and corresponding widths. X = = = WX = = The polygons ratio is 8, or 8 to. FLT similar. The similarity K L 3 1a. If you measure the angles in two figures and find that corresponding angles are not congruent, what conclusion can you draw about the figures? How is this a shortcut in determining if figures are similar? 3 N M P.2 etermine the ratios of the lengths of corresponding opposite sides. KL PQ = = KN PS = = The polygons similar, because There is no similarity ratio. Q S.2 hapter Lesson 1
2 1b. escribe how to find the similarity ratio of two similar figures when you are given lengths of corresponding sides. 2 PP FO -ST.1.1b XPLO Finding Unknown Lengths in Similar Polygons The trapezoids below are similar. 3 3 F H J.2 7 What ratio can you use to multiply the known length in trapezoid F to get the known length.2 in trapezoid HJ? The known length of a side of trapezoid HJ will be the and the corresponding side length of trapezoid F will be the that fraction. of a fraction of J F = = The required ratio is. Use this ratio as a multiplier to find the unknown side lengths in trapezoid HJ. HJ = HJ = F HJ = F H = H = H = = = = FLT 2a. The ratio you used in the xplore can be called the scale factor of the first figure to the second figure. omplete the following: To find the scale factor of two similar figures, use the ratio of a side length in the corresponding side length in the figure. figure to the 2b. How is a scale factor used to find unknown side lengths in the second figure? 2c. Suppose figure is similar to figure. How is the similarity ratio of to related to the scale factor of to? hapter Lesson 1
3 PTI orresponding angles in each pair are congruent. Use ratios of corresponding sides to tell whether the figures are similar. If so, identify the similarity ratio. 1. triangle X to triangle X 3 2. trapezoid JHLK to trapezoid F 2 J K 8 H L F 3. polygon MN to polygon STUV N M 20 2 S V T 1. The angles in rhombus are congruent to the corresponding angles in rhombus. The sides of rhombus are 7 units long. The sides of rhombus are 9 units long. xplain why the rhombuses are similar. U hapter Lesson 1
4 The figures in each pair are similar. Find the lengths of the sides in the second figure. Show your work.. quadrilateral quadrilateral PQS 1 8 Q P 1 S. polygon HT polygon NPJ x 2x x 3x T x 2x H N 3x P J 7.. In the diagram below, consider to be the first triangle and to be the second triangle Polygons WX and F are similar and k > 0. Identify the similarity ratio of WX to F and the scale factor. xplain. a X b c ka kd kb F kc W d hapter 7 28 Lesson 1
5 Name lass ate 7-1 dditional Practice Identify the pairs of congruent corresponding angles and the corresponding sides _ etermine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. If not, explain why not. 3. parallelograms FH and TUVW. and LMN Tell whether the polygons must be similar based on the information given in the figures... _ _ hapter 7 28 Lesson 1
6 Problem Solving hapter 7 28 Lesson 1
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