B. Given the pre-image, scale factor, and center of dilation, use a compass and straightedge to graph the image.

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1 L L J K J K Given the pre-image, scale factor, and center of dilation, use a compass and straightedge to graph the image. 1. The scale factor is 3 and the center of dilation is the origin.. The scale factor is and the center of dilation is the origin arnegie Learning, Inc MOULE : Investigating roportionalit

2 . Use coordinate notation to determine the coordinates of the image. 1. has vertices (1, ), (3, ), and (9, 7). What are the vertices of the image after a dilation with a scale factor of using the origin as the center of dilation?. EF has vertices (, ), E (, ), and F (3, 1). What are the vertices of the image after a dilation with a scale factor of 5 using the origin as the center of dilation? 3. GHI has vertices G (0, 5), H (, ), and I (3, 3). What are the vertices of the image after a dilation with a scale factor of 9 using the origin as the center of dilation?. JKL has vertices J (, ), K (1, 3), and L (7, 0). What are the vertices of the image after a dilation with a scale factor of 1 using the origin as the center of dilation? 5. has vertices (, ), (1, 1), and (, 10). What are the vertices of the image after a dilation with a scale factor of 1 using the origin as the center of dilation?. EF has vertices (5, 5), E (15, 10), and F (0, 10). What are the vertices of the image after a dilation with a scale factor of 1 5 using the origin as the center of dilation?. Eplain how ou know that each pair of triangles are similar. 1.. cm 3 cm 1 cm 1 cm arnegie Learning, Inc. 7 cm 1 cm MOULE : Investigating roportionalit

3 Name ate 3.. in. in. in. in. 5 in. 10 in F G H E I J arnegie Learning, Inc. 7. in. in. in. 3 in.. E : Skills ractice 5

4 E. etermine what additional information ou would need to prove that the triangles are similar using the given theorem. 1. What information would ou need to use the ngle-ngle Similarit Theorem to prove that the triangles are similar?. What information would ou need to use the Side-ngle-Side Similarit Theorem to prove that the triangles are similar? 35 0 m m 10 m 3. What information would ou need to use the Side-Side-Side Similarit Theorem to prove that these triangles are similar?. What information would ou need to use the Side-ngle-Side Similarit Theorem to prove that the triangles are similar? 1 cm cm 5 cm 5 in. 5 in. 9 in. 9 in. 1 cm 5. What information would ou need to use the Side-Side-Side Similarit Theorem to prove that these triangles are similar?. What information would ou need to use the ngle-ngle Similarit Theorem to prove that the triangles are similar? arnegie Learning, Inc. ft ft MOULE : Investigating roportionalit

5 Name ate F. etermine whether each pair of triangles is similar. Eplain our reasoning. 1. Y 10 d T 10. d d X 1 d Z S. N 3 in. 0 in. M O 5 in in. 3. V. K arnegie Learning, Inc. 10 m W 1 m.5 m X 3 ft J ft 5 ft I L.5 m 10 ft 1 ft H 7 ft G : Skills ractice 7

6 Name ate II. alculating orresponding arts of Similar Triangles. alculate the length of the indicated segment in each figure. 1. HJ bisects H. alculate HF.. LN bisects L. alculate NM. F 15 cm J 1 cm G in. L 5 in. H 1 cm K in. N M 3. bisects. alculate.. S bisects S. alculate S. 3 ft ft 9 m 1 m ft S 1 m arnegie Learning, Inc. 5. YZ bisects Y. alculate YW. cm Y. VX bisects V. alculate XW. U 9 ft V X cm Z 9 cm W 10 ft X ft W : Skills ractice 9

7 . Solve for. 1.. S 9 T E M Z arnegie Learning, Inc. cm 1 cm in. F in. G N 50 MOULE : Investigating roportionalit

8 Name ate. Marsha wants to walk from the parking lot through the forest to the clearing, as shown in the diagram. She knows that the forest ranger station is 15 feet from the flagpole and the flagpole is 350 feet from the clearing. How far is the parking lot from the clearing? learing Forest ranger station Flagpole Forest arking lot arnegie Learning, Inc. 5. Ell and Jeff are on opposite sides of a canon that runs east to west, according to the graphic. The want to know how wide the canon is. Each person stands 10 feet from the edge. Then, Ell walks feet west, and Jeff walks 30 feet east. ft 10 ft. Minh wanted to measure the height of a statue. She lined herself up with the statue s shadow so that the tip of her shadow met the tip of the statue s shadow. She marked the spot where she was standing. Then, she measured the distance from where she was standing to the tip of the shadow, and from the statue to the tip of the shadow. 10 ft 30 ft What is the width of the canon? Minh 5 ft ft 1 ft What is the height of the statue? : Skills ractice 53

9 III. roofs Using Similar Triangles. Use the diagram and given information to write a statement that can be justified using the roportional Segments Theorem, Triangle roportionalit Theorem, or its onverse. State the theorem used E 3.. a b arnegie Learning, Inc. 5 MOULE : Investigating roportionalit

10 Name ate 5.. E. cm H G 3.9 cm F F. cm 3. cm. Use the diagram and given information to write two statements that can be justified using the Triangle Midsegment Theorem. 1.. E V W arnegie Learning, Inc. Given: is a triangle. is the midpoint of. E is the midpoint of. T Given: ST is a triangle. V is the midpoint of T. W is the midpoint of S. S : Skills ractice 55

11 Name ate. Use the ight Triangle/ltitude Similarit Theorem to write three similarit statements involving the triangles in each diagram. 1.. H M G Z 3.. N K W L T U M N arnegie Learning, Inc. 5.. W X : Skills ractice 57

12 IV. ividing Segments b atios. etermine the midpoint of a line segment with each set of given endpoints. 1. (, 0) and (, ). (3, ) and (9, 10) 3. (7, ) and (3, ). (, 3) and (, 5) 5. (10, 1) and (0, ). (, 7) and (, 9). etermine the coordinates of the point that divides each directed segment into the given ratio : 3. 1 : arnegie Learning, Inc. 5 MOULE : Investigating roportionalit