Ext 6-8 Sampler

CorrespondingPartsof Similar Shapes 48 Grade8 Lesson15, 8ETeacherGuide 49 Objective32: To identify corresponding sides of similar figures. To find that the ratioof the corresponding sides of similar figures areproportional Materials: CentimeterGraphPaper (Master 8), base ten unit blocks Vocabulary: similar figures, dilation Models andPictures of Similar Figures Eachpair or small groupof studentswill need a sheet of CentimeterGraphPaper (Master 8) andbase tenunit blocks. Todaywewill buildmodels anddrawpicturesof a figureanda second figure thathas sides two times as long.Useyour cubes tobuilda rectangular solid thathas abasewitha lengthof 5 cmandwidthof 2 cm.Then outline thebaseonyourgraphpaper. Label the rectangle ABCD. Nowmakea second rectangular solidwithdimensions twiceas longas the first.Whatwill be the lengthand widthof this rectangular solid? (10 cm and4 cm) Outline thebaseof the solidonyourgraphpaperand label the rectangleasEFGH. Whenweenlargeor shrinka figure inaproportional way,wearedilating the shape. RectanglesABCDandEFGHare similar figures. Similar figureshave the same shapebutnot the same size. Writeon theboard: ABCD andEFGH are similar rectangles. RectangleEFGH is adilationof rectangleABCD. Corresponding sidesof similar figures are sides in the sameposition in similar figures. Name the corresponding sides toAB, BC,CD andDA. (EF, FG,GH,HE) Howare the corresponding sidesof similar figures related? (Eachof the sides ismultipliedordividedby the samenumber.) A B D C Base E F H G Base Writeon theboard: AB 2 =EF AD 2 =EH We say the corresponding sides areproportional or relatedby the same ratio.Aproportion is anequation showing that two ratios areequal. Writeon theboard: = A EF B = 1 5 0 = 1 2 = A EH D = 2 4 = 1 2 Read the information together at the topof thepage. Have students identify the corresponding sides of the two rectangles, then count theunits in the length andwidthof both rectangles. They shoulddiscover that the lengthof the sideof the larger rectangle is 3 times that of the smaller rectangle andvice versa. Solveproblem1with the class. Have students complete thepageon their own. Skill Builders 32-3, 32-5 lengthof small shape lengthof large shape widthof small shape widthof large shape 49 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. 1. dimension ratio AB EF EF = _______ _____ BC FG FG = _______ _____ 2. dimension ratio MN PQ PQ = _______ _____ MO PR PR = _______ _____ Ratios of corresponding sides: AB : EF BC : FG CD : DA : 4 : 12 2 : 6 CorrespondingParts of Similar Shapes Draw a similar figure that is double the length of each side of the original figure. Find the dimensions and the ratio of the corresponding sides. Draw square EFGH. Draw triangle PQR. A B C D M N O Similar polygons have congruent angles and proportional sides. Rectangle ABCD is similar to rectangle EFGH . Find the ratio of the corresponding sides. Draw a similar triangleDEFwith sides that are one-half the length of the sides of triangleABC. Find themissing dimensions and the ratio of the corresponding sides. 3. length of side corresponding to AB = ______ length of side corresponding to BC = ______ ratio of AB to corresponding side = ______ ratio of BC to corresponding side = ______ C B A ABC is similar to DEF . What is the length of DE ? A 3 B 5 C 8 D 10 4 12 = 2 6 24 = 24 We say that 4 is related to 12 in the same way that 2 is related to6. The corresponding sides are proportional. 4 : 12 2 : 6 4 4 1—2 1—2 1—2 6 4 1—2 2—= 4 2—= 4 2—= 4 8—= 4 6—= 3 3—= 6 4 3 2—1 2—1 G H R P Q F E D E F G—A H—E 8.G.4