Similar Figures B C F H S AD YZ ; _ RT. 6 cm. 3 cm


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1 107 imilar igures MIN I etermine whether figures are similar and find a missing length in a pair of similar figures. New Vocabulary similar figures corresponding sides corresponding angles indirect measurement Math Online glencoe.com tra amples ersonal utor elfheck Quiz he figures in each pair below have the same shape but different sizes. opy each pair onto dot paper. hen find the measure of each angle using a protractor and the measure of each side using a centimeter ruler. 1. 1, 5. on the smaller rectangle matches ee h. 10 nswer ppendi. on the larger rectangle. Name all pairs of matching sides in each pair of figures. he notation means the segment with endpoints at and. 2. rite each ratio in simplest form. he notation means the measure of segment. a. _ ; _ ; _ ; _ 1_ 1_ 1_ 1_ ; ; ; b. _ ; _ ; _ 2; 2; 2. hat do you notice about the ratios of matching sides?. Name all pairs of matching angles in the figures above. hat do you notice about the measure of these angles? 5. MK ONU about figures that have the same shape but not necessarily the same size. igures that have the same shape but not necessarily the same size are similar figures. In the figures below, triangle is similar to triangle. e write this as. 26 cm 6 cm cm 2 cm 26 cm cm 6 he matching sides are and, and, and and. he sides of similar figures that match are called corresponding sides. he matching angles are and, and, and and. he angles of similar figures that match are called corresponding angles. 50 hapter 10 eometry: olygons
2 he Mini Lab illustrates the following statements. imilar igures Key oncept ords Models If two figures are similar, then the corresponding sides are proportional, and the corresponding angles are congruent. eading Math eometry ymbols is similar to is congruent to ymbols he symbol means is similar to. corresponding sides: = _ = corresponding angles: ; ; Identify imilar igures 1 hich trapezoid below is similar to trapezoid? 1 Q 6 ind the ratios of the corresponding sides to see if they form a constant ratio M 10 K 5 L rapezoid Q rapezoid rapezoid KLM _ Q = _ 6 or _ 2 _ = KL = _ 5 _ = _ 12 1 or _ 6 _ 7 = _ 12 9 or LM = _ or _ 6 5 Not similar imilar Not similar o, trapezoid is similar to trapezoid. a. hich triangle below is similar to triangle? triangle Lesson 107 imilar igures 51
3 eading Math eometry ymbols ust as the measure of angle can be written as m, there is a special way to indicate the measure of a segment. he measure of is written as, without the bar over it. ind ide Measures of imilar riangles 2 If, find the length of. ince the two triangles are similar, the ratios of their corresponding sides are equal. rite and solve a proportion to find. _ = _ 6_ 18 = _ n 6n = 18 () 6n = 72 n = 12 rite a proportion. 6 m 18 m 5 m 15 m m Let n represent the length of. hen substitute. ind the cross products. implify. ivide each side by 6. he length of is 12 meters. b. If, find the length of. 21 ft 28 ft 5 ft ft ft 5 ft Indirect measurement uses similar figures to find the length, width, or height of objects that are too difficult to measure directly. Old aithful in ellowstone National ark shoots water 60 feet into the air that casts a shadow of 2 feet. hat is the height of a nearby tree that casts a shadow 6 feet long? ssume the triangles are similar. ft 6 ft 60 ft 2 ft ree Old aithful _ 6 = _ 60 2 height shadow 2 = 60 (6) ind the cross products. 2 =,780 implify. = 90 ivide each side by 2. he tree is 90 feet tall. c. OO estiny wants to resize a inch wide by 5inch long photograph for the school newspaper. It is to fit in a space that is 2 inches wide. hat is the length of the resized photograph? 2.5 in. in. 5 in. 2 in. 52 hapter 10 eometry: olygons
4 indicates multistep problem ample 1 (p. 51) ample 2 (p. 52) ample (p. 52) 1. hich rectangle below is similar to rectangle? rectangle Q Q 2 6 L ind the value of in each pair of similar figures m U 5 m V m 7 m. O flagpole casts a 20foot shadow. t the same time, umberto, who is 6 feet tall, casts a 5foot shadow. hat is the height of the flagpole? ssume the triangles are similar. 2 feet. 5 mm 1 mm 15 mm 20 ft 8 9 mm 6 ft 5 ft OMOK L or ercises L ee amples 1 2 ercise Levels : 5 12 : 1 17 : hich triangle below is similar to triangle? triangle 2 5 M N K L 6. hich parallelogram below is similar to parallelogram KM? parallelogram U 12 M K U 20 6 L ind the value of in each pair of similar figures. 7. Q 25 mi 8. 7 cm U 5 mi 6 mi 0 mi 1 cm V O 28 cm 1 cm Lesson 107 imilar igures 5
5 L ind the value of in each pair of similar figures m 18 m 12 in. in. 7.2 in. 5 in. 0.5 m 9 m 11. K uth is at the park standing net to a slide. uth is 5 feet tall, and her shadow is feet long. If the shadow of the slide is.8 feet long, what is the height of the slide? ssume the triangles are similar. 6 ft ft 5 ft.8 ft ft 12. UNIU child s desk is made so that it is a replica of a fullsize adult desk. uppose the top of the fullsize desk measures 5 inches long by 6 inches wide. If the top of a child s desk is 2 inches wide and is similar to the fullsize desk, what is the length? 6 in. 5 in. in. 2 in. in. 6 in. L ind the value of in each pair of similar figures. ealorld Link he height to the top of the lightning rod on the mpire tate uilding is 1,5 feet. ource: ired New ork m mm K 1 m 29. m 7.2 mm 5.1 mm.6 mm 25.2 m L M I I ee pages 695, hapter 10 eometry: olygons K or ercises 15 and 16, use the information below and at the left. ricia has a miniature replica of the mpire tate uilding. he replica is 10 inches tall, and the height of the observation deck is 8. inches. 15. bout how tall is the actual observation deck? 1,207 feet 16. ricia s sister has a larger replica in which the height of the observation deck is 12 inches. ow tall is the larger replica? about 1 inches 17. MUMN he ratio of the length of square to the length of square is : 5. If the length of square is 18 meters, what is the perimeter of square? 120 m
6 .O.. roblems LLN or ercises 18 and 19, use the following information. wo rectangles are similar. he ratio of their corresponding sides is 1 :. 18. ind the ratio of their perimeters. 1 : 19. hat is the ratio of their areas? 1 : 16 IIN IN 20. M rite a problem about a realworld situation that could be solved using proportions and the concept of similarity. hen use what you have learned in this lesson to solve the problem. ee students work. 21. hich rectangle is similar to the rectangle shown? ft 16 yd ft 2 in. 8 yd 1 in. 22. hich of the following equations is a correct use of crossmultiplication in solving the proportion _ = _ m 6? 12 m = = m = m = m oratio is 6 feet tall and casts a shadow feet long. hat is the height of a nearby tower if it casts a shadow 25 feet long at the same time? 28 yd 8 yd h 6 ft 12 m 25 ft ft m 25 feet 50 feet 5 feet 75 feet OM lassify the quadrilateral using the name that best describes it. (Lesson 106) 2. square 25. trapezoid 26. quadrilateral 27. MUMN triangularshaped sail has angle measures of and 67. ind the measure of the third angle. (Lesson 10) 69 QUII KILL olve each equation. (Lesson ) 28. 5a = = = 8n t = Lesson 107 imilar igures 55
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