7.4 Showing Triangles are
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1 age 1 of 7 7. howing riangles are imilar: and oal how that two triangles are similar using the and imilarity heorems. ey ords similar polygons p. he triangles in the avajo rug look similar. o show that they are similar, you can use the definition of similar polygons or the imilarity ostulate. In this lesson, you will learn two new methods to show that two triangles are similar. O 7.2 ide-ide-ide imilarity heorem () ords If the corresponding sides of two triangles are proportional, then the triangles are similar. ymbols If, then. 1 se the imilarity heorem etermine whether the triangles are similar. If they are similar, write a similarity statement and find the scale factor of riangle to riangle. olution ind the ratios of the corresponding sides Q Q 1 2 ll three ratios are equal. o, the corresponding sides of the triangles are proportional. y the imilarity heorem, Q. he scale factor of riangle to riangle is howing riangles are imilar: and 7
2 age 2 of 7 tudent elp I hen using the imilarity heorem, compare the shortest sides, the longest sides, and then the remaining sides. Is either or similar to? olution 2 se the imilarity heorem 1 ook at the ratios of corresponding sides in and. hortest sides ongest sides emaining sides ecause all of the ratios are equal,. 2 ook at the ratios of corresponding sides in and. hortest sides ongest sides emaining sides ecause the ratios are not equal, and are not similar. 1 se the imilarity heorem etermine whether the triangles are similar. If they are similar, write a similarity statement tudent elp OO o review included angles, see p. 22. O 7. ide-ngle-ide imilarity heorem () ords If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides that include these angles are proportional, then the triangles are similar. ymbols If aca and, then. 0 hapter 7 imilarity
3 age of 7 etermine whether the triangles are similar. If they are similar, write a similarity statement. olution se the imilarity heorem a and a both measure 1, so aca. ompare the ratios of the side lengths that include a and a. horter sides onger sides 1 0 he lengths of the sides that include a and a are proportional. y the imilarity heorem,. 1 1 how that. imilarity in Overlapping riangles tudent elp I edraw overlapping triangles as two separate triangles, as shown on p.. olution eparate the triangles, and, and label the side lengths. aca by the eflexive roperty of ongruence. horter sides onger sides he lengths of the sides that include a are proportional. y the imilarity heorem,. se the imilarity heorem etermine whether the triangles are similar. If they are similar, write a similarity statement. xplain your reasoning howing riangles are imilar: and 1
4 age of 7 7. xercises uided ractice ocabulary heck kill heck 1. If two sides of a triangle are proportional to two sides of another triangle, can you conclude that the triangles are similar? In xercises 2 and, determine whether the triangles are similar. If they are similar, write a similarity statement Is either or similar to? xplain. 7 1 ractice and pplications xtra ractice ee p.. imilarity heorem etermine whether the two triangles are similar. If they are similar, write a similarity statement and find the scale factor of riangle to riangle omework elp xample 1: xs., 21 2 xample 2: xs xample : xs. 1 1, 21 2 xample : xs. 1,, hapter 7 imilarity
5 age of 7 imilarity heorem Is either or similar to? xplain your reasoning rame uilding uppose you are constructing an -frame home that is modeled after a ski lodge. he ski lodge and home are shown below. re the triangles similar? xplain your reasoning. Itudent elp I O. O imilarity heorem etermine whether the two triangles are similar. If they are similar, write a similarity statement. OO xtra help with problem solving in xs. 1 is at classzone.com howing riangles are imilar: and
6 age of 7 tudent elp I edraw overlapping triangles as two separate triangles, as shown on p.. Overlapping riangles how that the overlapping triangles are similar. hen write a similarity statement etermining imilarity etermine whether the triangles are similar. If they are similar, state the similarity and the postulate or theorem that justifies your answer ports huffleboard In the portion of a shuffleboard court shown,. 27. hat piece of information do you need in order to show that using the imilarity heorem? 2. hat piece of information do you need in order to show that using the imilarity heorem? O is played on a long flat court. layers earn points by using sticks called cues to push circular disks onto a scoring area at the opposite end of the court. ou be the udge 2. on claims that is similar to when x. ave believes that the triangles are similar when x. ho is right? xplain your reasoning. x 1 21 hapter 7 imilarity
7 age 7 of 7 tandardized est ractice echnology In xercises 0 and 1, use geometry software to complete the steps below. 1 raw. 2 onstruct a line perpendicular to &* through. abel the intersection. easure &*, &*, &*, and &*. alculate the ratios and. rag point until. 0. or what measure of a are and similar? 1. hat theorem supports your answer to xercise 0? 2. ultiple hoice hich method can be used to show that the two triangles at the right are similar? annot be shown. ultiple hoice In the diagram,. ind the value of x x 1 ixed eview sing isectors In the diagram below, &*( bisects a. (esson.). &*c_?_.ac_?_ 27. ma _?_ 7. Is a congruent to a? xplain your reasoning. olving roportions olve the proportion. (esson 7.1) b y 0. c a lgebra kills riting ecimals as ractions rite the decimal as a fraction in simplest form. (kills eview, p. 7) howing riangles are imilar: and
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