Sections 8-3/8-5: April 24, 2012

Warm-up: (10 mins) Practice Book: Practice 8-2 # 1 – 23 (odd)

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 Side- Splitter 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-Angle- Bisector 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,  p. 448 # 1-3, 9-15 (odd), 25, 27, 32, 33 Homework (R)  p. 436 # 4-19,  p. 448 # 1-3, 9-15 (odd), 32, 33