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Spi.4.11 Use basic theorems about similar and congruent triangles to solve problems. Check.4.36 Use several methods, including AA, SSS, and SAS, to prove that two triangles are similar. CLE 3108.4.8 Establish processes for determining congruence and similarity of figures, especially as related to scale factor, contextual applications, and transformations. ""Thunder is good, thunder is impressive; but it is lightning that does the work." Mark Twain Angle-Angle (AA) Similarity Side-Side-Side (SSS) Similarity Side-Angle –Side (SAS) Similarity If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. PT and QS then PQRTSU If the measures of corresponding sides of two triangles are proportional, then the triangles are similar. Ex. PQ/ST= QR/SU=RP/UT so PQRTSU If the measures of two sides of a triangle are proportional to the measure of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar. Ex. PQ/ST= QR/SU and QS then PQRTSU Q S R P T U Q c a R b P S ax T R P T U bx Q c a cx S ax cx U In the figure, FGEG, BE=15, CF=20, AE=9 and DF=12. Determine which triangles are similar. C If you can show AE & BE proportional to DF and CF, then SAS Similarity to show triangles as similar B G A F FGE is an isosceles triangle so GFE GEF E D Two are proportional So ABE DCF In the figure, AB||DC, BE=27, DE = 45, AE = 21, CE=35. Determine which two triangles are similar CDE EBA because they are alternate interior angles C BEA CED, because they are vertical angles ABE CDE, because AA Similarity Check B E A D Find AE and DE C A x -1 2 Since AB|| CD ABEDCE and BAECDE because alternate interior angles B E 5 x+5 D ABE~DCE because of AA similarity ABE~DCE because of AA similarity 2(x+5) = 5(x – 1) 2x + 10 = 5x – 5 15 = 3x 5=x EA = x – 1 = 5 – 1 = 4 DE = x + 5 = 5 + 4 = 9 0.9 x = 1.2(240) 0.9x = 288 x = 288/.9=320 2 x = 12(242) 2x = 2904 x = 1452 Actual height 1450 Page 479, 10 – 24 even Notebook Check and Quiz Tomorrow