Presentation on theme: "By: THE “A” SQUAD (Annie and Andrew)"— Presentation transcript:
1By: THE “A” SQUAD (Annie and Andrew) CHAPTER 8: SectionsBy: THE “A” SQUAD(Annie and Andrew)
2Vocabulary TermsDilation: A transformation that is not rigid and preserves the shape of an object despite size changes.Scale Factor: The number that both X and Y are multiplied by to get the Image.Similar Figures: Figures are similar when the image of the other is congruent by a dilation.
3Postulates and Theorems Polygon Similarity Postulate: Two polygons are similar if and only if there is a way of setting up a correspondence between their sides and angles such that each pair of corresponding angles is congruent and each pair of corresponding sides is proportional.Angle-Angle Postulate: If two angles are congruent to two angles of another triangle, then the triangles are similar.Side-Side-Side Theorem: If three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.Side-Angle-Side Theorem: If two sides and their included angle are proportional/congruent respectively, then the triangles are similar.
4Examples: A D 14 Given: AB= 8; BC= 3; AC= 14; DE= 4; EF= 1.5; DF= 7 Prove: Triangle ABC ~ Triangle DEF874EFBC31.5AB/DE= 8/4= 2 BC/EF= 3/1.5= AC/DF= 14/7= 2Thus, the sides of the triangles are proportion and, by the SSS Similarity Theorem, Triangle ABC ~ Triangle DEF.
5More Examples:Given: <x = 25; <g = 25; xy = 2; xz = 3.6; fg= 3; gh = 5.4Prove: Triangle XYZ ~ Triangle GFHgx252523.65.43yzfhYX/FG = 2/3 XZ/GH = 3.6/5.4 = 2/3Thus, the sides of the triangle are proportional, and the included angles of these sides are congruent. By the SAS Similarity Theorem, Triangle QRS ~ Triangle UTV.