8.3 Start Thinking. 8.3 Warm Up. 8.3 Cumulative Review Warm Up
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1 .3 tart hinking carpentr class is working on a project for the local childcare centers. he students are making wooden trees to go with the centers train sets. he work from a sample that was cut from a three-inch tall triangular block of wood. he goal is to make more trees, proportional to the sample, but larger. Use the diagrams below to determine the lengths of the sides and of the triangles for trees made from four-inch and five-inch blocks of wood ample.3 arm Up Use the diagram to cop and complete the statement m = 4. m =. m = umulative eview arm Up rite an equation of the line passing through point that is perpendicular to the given line. 1. ( 0, 3 ), = 2. ( ) 2, 4, ( ) 4, 0, = 9 + = 4. ( 2, 1 ), = ( + 3) 3 2 opright ig Ideas Learning, LL ll rights reserved. esources b hapter 273
2 Name ate.3 ractice 1. etermine whether or is similar to In ercises 2 and 3, find the value of that makes KL L 3 K 13. L 3 K 4. erif that U. ind the scale factor of U to. U: U =, U = 21, = 1 : = 3, = 49, = 42 In ercises and 6, show that the triangles are similar and write a similarit statement. plain our reasoning L 21 N In ercises 7 11, use the diagram to cop and complete the statement. 7.. m = m =. m = 11. = In the figure for ercises 7 11, is? plain our reasoning Use the figure to write a two-column proof. iven: = rove: 274 opright ig Ideas Learning, LL esources b hapter ll rights reserved.
3 Name ate.3 ractice In ercises 1 and 2, find the value of that makes erif that KL. ind the scale factor of KL to. KL: K =, KL = 30, L = 2 : =, = 24, = In ercises 4 and, show that the triangles are similar and write a similarit statement. plain our reasoning L N 6. has side lengths 42, 21, and 3 units. he shortest side of a triangle similar to is 9 units long. ind the other lengths of the triangle. 7. Use the figure to find the values of,, and z that makes H H 14 2( 4) 6z + Use the figure to write a two-column proof. iven: = rove: 9. iven: LN = 2 N = N = N = rove: LN N 2 L N 2 opright ig Ideas Learning, LL ll rights reserved. esources b hapter 27
4 Name ate.3 nrichment and tension roving riangles imilar b and 1. In the figure,. a. ind the scale factor of to b. ind the ratio of the area of to the area of ( ) = ( + ), and that m ( 2 ), m 2. iven HI, m = 0, m = 2 +, m I = find I. 3. portion of a water slide in an amusement park is shown. ind the length of, if the posts and form a right angle with the ground 40 ft 2 ft 4. streetlight is mounted at the top of a -foot pole. 6-foot man walks awa from the pole along a straight path. How long is his shadow when he is 40 feet from the pole?. Use the information and the diagram to prove the statement. iven: H and H rove: K K K H 276 opright ig Ideas Learning, LL esources b hapter ll rights reserved.
5 Name ate.3 uzzle ime hat peaks ver Language? ircle the letter of each correct answer in the boes below. he circled letters will spell out the answer to the riddle. omplete the sentence. 1. If the corresponding side lengths of two triangles are, then the triangles are similar. 2. If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are. 3. If two nonvertical lines are, then the have the same slope. 4. If two lines are perpendicular, then the product of their slopes is 1. Name the triangle that is not similar.. 3 K 24 L K 42 L H I N K proportional concurrent parallel KL O H O congruent perpendicular similar equal KL nonvertical opright ig Ideas Learning, LL ll rights reserved. esources b hapter 277
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