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 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, 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