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Name _______________________________ Date ___________ Geometry Congruent and Similar Figures Write three conditions that two congruent polygons must share. 1. They have the same shape and size. 2. Their corresponding angles have the same measure. 3. Their corresponding sides have the same measure. These two triangles are congruent. Draw slash marks to show which are the corresponding sides and angles. Write an equation stating that the two triangles are congruent. Be sure to name both triangles by their corresponding vertices. Students may name the first triangle in any order, but their equation should reflect the corresponding vertices. Correct answers include the following: ∆ CDE ≅ ∆ STR ∆ DCE ≅ ∆ TSR ∆ ECD ≅ ∆ RST ∆ EDC ≅ ∆ RTS Tell how to find the measure of RS . Use the measure of its corresponding part, side EC from ∆ ECD. Write the name of each corresponding part. EC RS = ________ DE TR = ________ ∠C ∠ S = ________ ∠E ∠ R = ________ Write the measure of each corresponding part. 9 RS = ________ © 2003 CompassLearning, Inc. TR = ________ 8.5 63° ∠ S = ________ Page 1 90° ∠ T = ________ Activity 8085/8127 Name _______________________________ Date ___________ Geometry Congruent and Similar Figures These two quadrilaterals are congruent. Fill in the blanks. KLMJ CDAB ≅ ___________ BADC JMLK ≅ ___________ Use corresponding parts to find the missing measures. 6 AB = ________ 2 DC = ________ 7 JK = ________ 4 ML = ________ 45° ∠ D = ________ 25° ∠ B = ________ 155° ∠ K = ________ 135° ∠ M = ________ Describe the ways in which two similar polygons are alike and different. Two similar polygons have the same shape, but they may differ in size. Their corresponding angles have the same measure. Their corresponding sides are proportional. © 2003 CompassLearning, Inc. Page 2 Activity 8085/8127 Name _______________________________ Date ___________ Geometry Congruent and Similar Figures These two quadrilaterals are similar. Fill in the blanks. OLMN GFED ≈ ___________ FGDE LONM ≈ ___________ Tell how to find the measure of ∠ O of the quadrilateral above. Use the measure of its corresponding part, ∠ G, from quadrilateral GFED. Write the name of each corresponding angle. ∠O ∠ G = ________ ∠N ∠ D = ________ ∠M ∠ E = ________ ∠L ∠ F = ________ Write the measure of each corresponding angle. 92° ∠ D = ________ 150° ∠ F = ________ 64° ∠ O = ________ 54° ∠ M = ________ The corresponding sides of similar figures are proportional. Write the names of the corresponding sides of the two quadrilaterals above. ON GD ≈ ________ © 2003 CompassLearning, Inc. NM DE ≈ ________ ML EF ≈ ________ Page 3 NM FG ≈ ________ Activity 8085/8127 Name _______________________________ Date ___________ Geometry Congruent and Similar Figures How do you find missing lengths of sides of similar figures? Write a proportion that compares the corresponding sides. Write and solve a proportion to find the length of LO of the quadrilateral above. Show your work. Round your answer to the nearest tenth. 15 16 = 5 n 16 x 5 = 15n 80 = 15n 80 = n 15 n = 5.3 LO = 5.3 Write and solve a proportion to find the length of ON of the quadrilateral above. Show your work. 15 9 = 5 n ON = 9 x 5 = 15n 45 = 15n 45 = n 15 n=3 3 © 2003 CompassLearning, Inc. Page 4 Activity 8085/8127