Ext 6-8 Sampler

49 Grade8 WordProblemswithSimilar Figures Lesson15, 8ETeacherGuide 50 Objective46: To solvewordproblems involving similar figures. Materials: CentimeterGraphPaper (Master 8) Vocabulary: indirectmeasurement CorrespondingSides of Similar Figures Each small grouporpair of students shouldhave a sheet ofCentimeterGraphPaper (Master 8). Writeonboard: At noon a small childwho is 2 feet tall casts a shadow3 feet long.At the same time, aman casts a9-foot shadow.How tall is theman? Useyourgraphpaper tohelpyou solve theproblem. Firstdrawapictureof the childand the child’s shadowon yourgraphpaper.You candraw the third side to completea right triangle. Nowdrawa secondpictureof theman’s9-foot shadow onyourgraphpaper.How tall shouldyoudraw theman? Howdoyouknow? (Theman is 6 feet tall. Since the shadowof theman is 3 times longer than the shadowof the child, theheight of theman should alsobe3 times the height of the child.) These two triangles are similar.What is the special relationshipbetween the corresponding sidesof similar figures? (The sides areproportional.) This is anexample of indirectmeasurement.Wedonot actuallyusea measuring instrument to find theheight.Weuse proportional reasoning. Writeon theboard: Marteenwants toknow theheight of a tall tree. Marteen is 6 feet tall and casts a shadow2 feet long at the same time the tree casts a shadow 7 feet long.How tall is the tree? 3' 2' Child 9' 6' Man Drawapicture.Writeaproportion to find theheight of the tree. Read the illustration together, pointingout that the triangles are similar because the sunmeets the topof the tree and the fencepost at the same angle. Finish the problem. Ask student volunteers to read anddraw a sketchof the similar figures inproblems 1 and3.Have students complete thepageon their own. Skill Builders 46-2, 46-3 6' 7' 2' 6 2 x x 7 = 2 • x =6 • 7 2 x =42 x = 21 ft. 50 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. 1. 3. A tree casts a shadow of 25m at the same time a 4m pole casts a 1m shadow. How high is the tree? ______________ 5. Amonument casts a 78 ft. shadow at the same time that a vertical yardstick casts a 4.5 ft. shadow. How high is themonument? ______________ 7. A person 72 in. tall casts a 54 in. shadow at the same time that a building casts a 30 ft. shadow. How tall is the building? ______________ 2. 4. A building casts a 36 ft. shadow at the same time that a vertical yardstick casts a shadow of 2 ft. How tall is the building? ______________ 6. The sides of a triangle are 3, 4 and 5 cm. What are the lengths of the sides of a similar trianglewhose smallest sidemeasures 7.5 cm? ______________ 8. The ratio of two numbers is 2 to 5. If the smaller number is 60, what is the larger number? ______________ WordProblemswithSimilar Figures A fence 2 ft. tall casts a 4 ft. shadow at the same time that a tree casts a 20 ft. shadow. How tall is the tree? The triangles are similar, so the sides form a proportion. 2__ 4 = x __ 20 4 x = 40 x = _____ ft. The tree is ____ ft. tall. x = _____ x = _____ The pairs of triangles are similar. Find the length of x . 21 21 3 x x 7 4.5 3.5 x 10 40 3 100m 54 ft. 40 ft. 150 52 ft. 7.5, 10 and 12.5 cm 9 7.RP.3