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Name _______________________________________ Date ___________________ Class __________________ Practice A Ratio in Similar Polygons Fill in the blanks to complete each definition. 1. A similarity ratio is the ratio of the lengths of the ____________________ sides of two similar polygons. 2. Two polygons are similar if and only if their corresponding angles are ____________________ and their corresponding sides are.____________________. 3. Figures that are similar have the same shape but not necessarily the same ____________________. Use the figure for Exercises 4 and 5. The triangles are similar. 4. Name the pairs of congruent angles. A ____________________ B ____________________ C ____________________ 5. Write the corresponding side lengths in the proportion below. AB DE FD Use the figure for Exercises 6 and 7. The triangles are similar. 6. Circle the correct similarity statement. QRS KJL RSQ KJL QSR LKJ 7. Write a proportion with all three pairs of corresponding side lengths. _______________________________________ Use the figure for Exercises 8 and 9. 8. Tell why the corresponding angles in the rectangles are congruent. __________________________________________________________ __________________________________________________________ 9. Substitute numbers for the side lengths and reduce each ratio to simplest form. DE DG ______ __________ LM MN _____________ © Houghton Mifflin Harcourt Publishing Company Holt McDougal Analytic Geometry Name _______________________________________ Date ___________________ Class __________________ Reading Strategies 14. midsegment triangle 1. rectangle 2. rhombus 3. square 4. rectangle 5. square 6. rhombus 7. rhombus RATIOS IN SIMILAR POLYGONS Practice A 1. corresponding Reteach 2. congruent; proportional 1. valid E 3. valid 5. 4. Not valid; need to know that EFGH is a . 5. rhombus 6. rectangle, rhombus, square 7. rectangle 8. rectangle, rhombus, square Challenge 7. a. The measure of each angle should be 108. All the sides should be congruent. b. Results will vary. 8. Proceed as in Exercises 1–5. Draw bisectors of all sides of pentagon; mark intersection of bisectors and the circle as the other 5 points of the decagon; draw line segments. 9. Choices will vary. Problem Solving 1. Diagonals bisect each other, so the quad. is a . The diagonals are , so EFGH is a rect. because with diags. rect. 2. No; from the given information, you can conclude only that ABCD is a rhombus. 3. Both pairs of opposite sides are , so STUV is a . STUV is a rectangle because with diags. rect. 4. A 6. D 4. F 3. size 2. Not valid; need to know that MPQR is a . 7. D AB CB AC FE DE FD KJL 6. RSQ RS SQ QR KJ JL LK 8. Possible answer: Every angle in a rectangle is a right angle, and all right angles are congruent. 9. 4 5 10. 8 4 ; 10 5 Practice B 1. A X; B Z; C Y; AC AB BC 2 XY XZ ZY 3 2. H Q; I R; J S; K P; KJ KH HI JI 5 PS PQ QR SR 4 7 ; Possible answer: 5 WTUV 3. yes; EFGH 4. No; sides cannot be matched to have corresponding sides proportional. 5. yes 6. yes 7. no 8. yes 5. F 7. G © Houghton Mifflin Harcourt Publishing Company Holt McDougal Analytic Geometry