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Transcript
January 17, 2017 HF: Obj: To apply properties of trapezoids. Write or circle the problems you have a question on. To apply properties of kites. (HR) (6.6)Pg.444: 9, 11, 13, 24-27, 41-49odd, 52-57, 60, 66 Statement Reason January 17, 2017 January 17, 2017 January 17, 2017 January 17, 2017 January 17, 2017 A triangle's angles are in the ratio 2:3:4. What are the measures of the angles? January 17, 2017 (7.2) Similar Polygons (7.3) (Similar Triangles) Objective: To use proportions to identify similar polygons. To solve problems using properties of similar polygons. To prove Triangles Similar and find missing parts. Why: Enlarging/Reducing objects is important in many applications (logos, signs, blueprints, etc) January 17, 2017 Obj: To use proportions to identify similar polygons. To solve problems using properties of similar polygons. To prove triangles similar and find missing parts. Similar Polygons: ABCD ~ WXYZ B W Z A X C Y D Find n, x, and y. ABCD ~ WXYZ B A 12 o (y+34) 83o Z 9 C x D Are the figures similar? Explain. 6 W (3y- 1 3) o 10 Y X 3n-1 January 17, 2017 Obj: To use proportions to identify similar polygons. To solve problems using properties of similar polygons. To prove triangles similar and find missing parts. January 17, 2017 Obj: To use proportions to identify similar polygons. To solve problems using properties of similar polygons. Ways to Prove Triangles Similar: To prove triangles similar and find missing parts. 1. Angle-Angle (AA) Similarity Postulate: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. F C If then ABC~ DEF A B E D 2. Side-Side-Side (SSS) Similarity Theorem: If corresponding side lengths in two triangles are proportional, then the triangles are similar. F C A B AB If DE = BC EF = E D AC then FD ABC~ DEF 3. Side-Angle-Side (SAS) Similarity Theorem: If 2 sides of one triangle are proportional to 2 sides of another triangle, and their included angles are congruent, then the triangles are similar. F C A If AC DF B = AB DE E D and A = D then ABC~ DEF January 17, 2017 Obj: To use proportions to identify similar polygons. To solve problems using properties of similar polygons. To prove triangles similar and find missing parts. January 17, 2017 Obj: To use proportions to identify similar polygons. To solve problems using properties of similar polygons. To prove triangles similar and find missing parts. First, prove ABE ~ ACD. Then find x and y. January 17, 2017 Obj: To use proportions to identify similar polygons. Find x. To solve problems using properties of similar polygons. To prove triangles similar and find missing parts. January 17, 2017 Obj: To use proportions to identify similar polygons. To solve problems using properties of similar polygons. HW: To prove triangles similar and find missing parts. (HR): (7.2) Pg.474: 19, 23, 24, 36, 37 (7.3) Pg.483: 9, 11, 12, 17, 18, 23