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6.3 Similar Triangles

6.3 Similar Triangles. What you’ll learn: To Identify similar triangles To use similar triangles to solve problems. Postulate 6.1. Angle-Angle (AA) Similarity If the 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar. Ex: If AD and

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6.3 Similar Triangles

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  1. 6.3 Similar Triangles What you’ll learn: To Identify similar triangles To use similar triangles to solve problems

  2. Postulate 6.1 Angle-Angle (AA) Similarity If the 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar. Ex: If AD and BE, then ABCDEF because of AA~ D A B E C F

  3. Theorems 6.1 Side-Side-Side (SSS) Similarity If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar. 6.2 Side-Angle-Side (SAS) Similarity If the measures of 2 sides of a ∆ are proportional to the measures of 2 corresponding sides of another triangle and the included angles are congruent, then the triangles are similar. 6 3 2 8 3 9 110 110 6 12 4 9

  4. Theorem 6.3 Similarity of triangles is reflexive, symmetric, and transitive. Reflexive:ABC~ABC Symmetric: If ABC~DEF then DEF~ABC Transitive: If ABC~DEF and DEF~GHI, then ABC~GHI.

  5. In the figure, ABDC, BE=27, DE=45, AE=21, and CE=35. Determine which triangles in the figure are similar. ABE~CDE C B E D A

  6. R Given RSUT, RS=4, RQ=x+3, QT=2x+10, UT=10, find RQ and QT. RQ=8 QT=20 4 x+3 S Q U 2x+10 10 T

  7. Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 p.m. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower’s shadow and it was 242 feet at that time. What is the height of the Sears Tower? x 12 2 242

  8. Homeworkp. 30210-28 even

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