7-2 Skills Practice. Similar Polygons. Determine whether each pair of figures is similar. Justify your answer.

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2 IO 7-2 kills ractice imilar olgons etermine whether each pair of figures is similar. Justif our answer Z 7.5 W Y X 7.5 ach pair of polgons is similar. Write a similarit statement, and find x, the measure(s) of the indicated side(s), and the scale factor.. G H. and U 5. W 6. and U 7 H 6 x x 1 10 V 1 W G Y L W 10 X x 2 U x 1 opright Glencoe/cGraw-Hill, a division of he cgraw-hill ompanies, Inc. hapter 7 Glencoe Geometr

3 IO 7- Lesson eading Guide imilar riangles Get ead for the Lesson ead the introduction to Lesson 7- in our textbook. What does it mean to sa that triangular shapes result in rigid construction? What would happen if the shapes used in the construction were quadrilaterals? ead the Lesson 1. tate whether each condition guarantees that two triangles are congruent or similar. If the condition guarantees that the triangles are both similar and congruent, write congruent. If there is not enough information to guarantee that the triangles will be congruent or similar, write neither. a. wo sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle. b. he measures of all three pairs of corresponding sides are proportional. c. wo angles of one triangle are congruent to two angles of the other triangle. d. wo angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of the other triangle. e. he measures of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle, and the included angles are congruent. f. he three sides of one triangle are congruent to the three sides of the other triangle. g. he three angles of one triangle are congruent to the three angles of the other triangle. h. One acute angle of a right triangle is congruent to one acute angle of another right triangle. i. he measures of two sides of a triangle are proportional to the measures of two sides of another triangle. 2. Identif each of the following as an example of a reflexive, smmetric, or transitive propert. a. If UVW, then UVW. b. If UVW and UVW O, then O. c. emember What You Learned. good wa to remember something is to explain it to someone else. uppose one of our classmates is having trouble understanding the difference between for congruent triangles and for similar triangles. How can ou explain the difference to him? opright Glencoe/cGraw-Hill, a division of he cgraw-hill ompanies, Inc. hapter 7 20 Glencoe Geometr

4 IO 7- tud Guide and Intervention imilar riangles Identif imilar riangles Here are three was to show that two triangles are similar. imilarit imilarit imilarit wo angles of one triangle are congruent to two angles of another triangle. he measures of the corresponding sides of two triangles are proportional. he measures of two sides of one triangle are proportional to the measures of two corresponding sides of another triangle, and the included angles are congruent. xample 1 etermine whether the xample 2 etermine whether the triangles are similar. triangles are similar b imilarit , so. m m, so. b imilarit. xercises opright Glencoe/cGraw-Hill, a division of he cgraw-hill ompanies, Inc. etermine whether each pair of triangles is similar. Justif our answer Lesson 7- hapter 7 21 Glencoe Geometr

5 IO 7- tud Guide and Intervention (continued) imilar riangles Use imilar riangles imilar triangles can be used to find measurements. xample 1. xample 2 person 6 feet tall casts ind x and. a 1.5-foot-long shadow at the same time that a flagpole casts a 7-foot-long shadow. How tall is the flagpole? 1 x x 1 1 1x (1 ) x ft 6 ft 7 ft? he sun s ras form similar triangles. Using x for the height of the pole, 6 x 1.5, 7 so 1.5x 2 and x 2. he flagpole is 2 feet tall. xercises ach pair of triangles is similar. ind x and x x x 6 x x x 22 opright Glencoe/cGraw-Hill, a division of he cgraw-hill ompanies, Inc. 7. he heights of two vertical posts are 2 meters and 0.5 meter. When the shorter post casts a shadow that is 0.5 meter long, what is the length of the longer post s shadow to the nearest hundredth? hapter 7 22 Glencoe Geometr

6 IO 7- kills ractice imilar riangles etermine whether each pair of triangles is similar. Justif our answer. 1. Y W X U J K 0 LG Identif the similar triangles, and find x and the measures of the indicated sides. 5. and 6. J L and L opright Glencoe/cGraw-Hill, a division of he cgraw-hill ompanies, Inc. J x 1 x 1 15 K 7. H and. V and H x 6 1 V 6 x 6 G U L x Lesson 7- hapter 7 2 Glencoe Geometr

7 IO 7- ractice imilar riangles etermine whether each pair of triangles is similar. Justif our answer. 1. J 2. Y W K L LG Identif the similar triangles, and find x and the measures of the indicated sides.. L and. L and L L x 1 x 1 J K 6x 2 L Use the given information to find each measure. 5. If, 6, x 7, 6. If H I,, G x 1,, and x 1, HI, and HG x, find and. find G and HG. II U or xercises 7 and, use the following information. lighthouse casts a -foot shadow. nearb lamppost that measures 5 feet inches casts an -foot shadow. 7. Write a proportion that can be used to determine the height of the lighthouse. G I H opright Glencoe/cGraw-Hill, a division of he cgraw-hill ompanies, Inc.. What is the height of the lighthouse? hapter 7 Glencoe Geometr

8 7- IO Word roblem ractice imilar riangles 1. IIU arla likes her chair so much that she decides to make a miniature replica of it for her pet hamster. ind the value of x. 15. HOW radio tower casts a shadow feet long at the same time that a vertical ardstick casts a shadow half an inch long. How tall is the radio tower? 1 2. OL Jim has a scale model of his sailboat. he figure shows drawings of the original sailboat and the model. ind x. 20 in. x in. x.5 OUI K or xercises 5 and 6, use the following information. Gavin and rianna want to know how far a mountain peak is from their houses. he measure the angles between the line of site to the peak and to each other s houses and carefull make the drawing shown. Gavin in. rianna 2 in in. eak 52 he actual distance between Gavin and rianna s house is miles. opright Glencoe/cGraw-Hill, a division of he cgraw-hill ompanies, Inc in.. GOY Georgia draws a regular pentagon and starts connecting its vertices to make a 5-pointed star. fter drawing three of the lines in the star, she becomes curious about two triangles that appear in the figure, and. he look similar to her. rove that this is the case. 52 in. 5. What is the actual distance of the mountain peak from Gavin s house? ound our answer to the nearest tenth of a mile. 6. What is the actual distance of the mountain peak from rianna s house? ound our answer to the nearest tenth of a mile. Lesson 7- hapter 7 25 Glencoe Geometr