Similarity Review (Unit 4)
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1 Similarity Review (Unit 4) Name Using a compass and straightedge construct the image of the figure after a dilation with point C as the center of dilation and the given scale factor. Label the vertices of the image using prime notation. 1. k = 3 2. k = ½ S F W N O U N 3. k = 2 4. k = 4 Q G T S R P A
2 5) In the table, compare the properties of the following transformations: reflections, translations, rotations and dilations. Check all that apply. Preserves Distance Preserves Angle Measure Preserves Betweenness Preserves Collinearity Rigid Motion REFLECTIONS TRANSLATIONS ROTATIONS DILATIONS 6) Dilate ΔABC with the given vertices using the given scale factor k and center (0,0). Draw ΔABC and the image of ΔABC. A(-8, 4), B(4, 2), C(0, -8); k = Pre-Image (x, y) Image (x, y) ( ) 7) Dilate ΔABC with the given vertices using the given scale factor k and center (0,0). Draw ΔABC and the image of ΔABC. A(-1,2), B(2, 3), C(2, -2); k = 3 Pre-Image (x, y) Image (x, y) ( )
3 8) Show the two given circles are similar by stating the necessary transformations from C to D. Provide coordinate C: center (0,0) radius 2; D: center (-3,-6) radius 4. Circle C is mapped to circle D by 9) Show the two given circles are similar by stating the necessary transformations from C to D. Provide coordinate C: center (-3, -3) radius 6; D: center (6, 5) radius 2. Circle C is mapped to circle D by 10) Show the two given triangles are similar by stating the necessary transformations. Provide coordinate
4 11) Show the two given figures are similar by stating the necessary transformations. Provide coordinate 12) Show the two given triangles are similar by stating the necessary transformations. Provide coordinate 13) Show the two given figures are similar by stating the necessary transformations. Provide coordinate 14) Show the two given figures are similar by stating the necessary transformations. Provide coordinate
5 15) Show the two given triangles are similar by stating the necessary transformations. Provide coordinate A(6,3), B(9,3), C(3,-3) D(0, 3), E(1, 5), F(2, 5) is mapped to by 16) Show the two given figures are similar by stating the necessary transformations. Provide coordinate Q(-1, 0), R(-2, 2), S(1, 3), T(2, 1) W(0, 2), X(4, 4), Y(6, -2), Z(2, -4) is mapped to by 17. To find the height of a dinosaur in a museum, Jack placed a mirror on the ground 40ft from the base. Then he stepped back 4ft so that he could see the top of the dinosaur in the mirror. Jack s eyes were approximately 5ft 6in above the ground. What is the height of the dinosaur?
6 18. Danielle is 5ft 2in tall. To find the height of the light pole, she measured her shadow and the pole s shadow at the same time of day. a. Approximate the height of the pole. b. Danielle s friend is standing next to her and she is 5ft 8in tall. How long is her shadow? 19. You are visiting the Unisphere at Flushing Meadows Corona Park in New York. To estimate the height of stainless steel model of Earth, you place a mirror on the ground and stand where you can see to top of the model in the mirror. a. Use the diagram to estimate the height of the model. b. Explain why this method works. 20) Sarah is standing in her back yard and she decides to estimate the height of a tree. She stands so that the tip of her shadow coincides with the tip of the tree s shadow, as shown. Sarah is 66 inches tall. The distance from the tree to Sarah is 95 feet and the distance between the tip of the shadows and Sarah is 7 feet. a. What criterion can you use to show that the triangles in the diagram are similar? b. About how tall is the tree? c. Andy is 75 inches tall. At a different time of day, he stands so that the tip of his shadow and the tip of the tree s shadow coincide as described above. His shadow is 6 feet long. How far is Andy from the tree?
7 21) Miles is proving that the AA Similarity Criterion follows from the definition of similarity in terms of similarity transformations. Help Miles by completeing the proof. GIVEN: A D and B E PROVE: ABC ~ DEF 22) The original photograph shown is 4 inches by 6 inches a. You dilate the original photograph by a scale factor of ½. What are the dimensions of the new photograph? b. You have a frame that holds photos that are 8.5 inches by 11 inches. Can you dilate the original photograph to fit the frame? Explain your reasoning. 23) You are making a scale model of a rectangular park for a school project. Your model has a length of 2 feet and a width of 1.4 feet. The actual park is 800 yards long. a. Find the scale factor of the scale model to the actual park. b. What is the perimeter of the scale model of the park and the perimeter of the actual park?
8 Find the values of the variables that make the triangles similar. 24) 25) 2y + 2 3x 1 4z 26) 27) A) Determine whether the triangles are similar. B) If they are similar, write a similarity statement and C)state the triangle similarity criterion that justifies your answer. If they are not similar, explain why not. 28) 29) A. A. B. B. C. C. 30) A E F 31) B M C B D A. H S S U A. B. B. C. C.
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