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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 Side-Splitter and Triangle-Angle-Bisector Theorems.
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.
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?
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