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Sections 8-3/8-5: April 24, 2012 Warm-up: (10 mins) Practice Book: Practice 8-2 # 1 – 23 (odd) Warm-up: (10 mins) Warm-up: (10 mins) Questions on Homework? Review Name the postulate you can use to prove the triangles are congruent in the following figures: Sections 8-3/8-5: Ratio/Proportions/Similar Figures Objective: Today you will learn to prove triangles similar and to use the SideSplitter and Triangle-Angle-Bisector Theorems. Angle-Angle Similarity (AA∼) Postulate Geogebra file: AASim.ggb Angle-Angle Similarity (AA∼) Postulate Example 1: Using the AA∼ Postulate, show why these triangles are similar ∠BEA ≅∠DEC because vertical angles are congruent ∠B ≅∠D because their measures are both 600 ΔBAE ∼ ΔDCE by AA∼ Postulate. SAS∼ Theorem ΔABC ∼ ΔDEF SAS∼ Theorem Proof SSS∼ Theorem SSS∼ Theorem Proof Example 2: Explain why the triangles are similar and write a similarity statement. Example 3: Find DE Real World Example How high must a tennis ball must be hit to just pass over the net and land 6m on the other side? Use Similar Triangles to find Lengths Use Similar Triangles to Heights Section 8-5: Proportions in Triangles Open Geogebra file SideSplitter.ggb Side-Splitter Theorem Example 4: Use the Side-Splitter Theorem to find the value of x Example 5: Find the value of the missing variables Corollary to the Side-Splitter Theorem Example 6: Find the value of x and y Example 7: Find the value of x and y Sail Making using the Side-Splitter Theorem and its Corollary What is the value of x and y? Triangle-Angle-Bisector Theorem Triangle-Angle-Bisector Theorem Proof Example 8: Using the Triangle-AngleBisector Theorem, find the value of x Example 9: Fnd the value of x Theorems Angle-Angle Similarity (AA∼) Postulate: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Side-Angle-Side Similarity (SAS∼) Theorem: If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar. Side-Side-Side Similarity (SSS∼) Theorem: If the corresponding sides of two triangles are proportional, then the triangles are similar. Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. Corollary to the Side-Splitter Theorem: If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional. Triangle-Angle-Bisector Theorem: If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle. Wrap-up Today you learned to prove triangles similar and to use the Side-Splitter and Triangle-Angle-Bisector Theorems. Tomorrow you’ll learn about Similarity in Right Triangles Homework (H) p. 436 # 4-19, 21, 24-28 p. 448 # 1-3, 9-15 (odd), 25, 27, 32, 33 Homework (R) p. 436 # 4-19, 24-28 p. 448 # 1-3, 9-15 (odd), 32, 33