Lesson 5A.2: Proving Similar Triangles SECTIONS 5.4.1 AND 5.4.2

Introduction 5.4.1 •There are many ways to show that two triangles are similar, just as there are many ways to show that two triangles are congruent. The Angle-Angle (AA) Similarity Statement is one of them.

•In this lesson we will prove that triangles are similar using similarity statements.

•Similarity statements identify corresponding parts just like congruence statements do.

Side-Angle-Side (SAS) The Side-Angle-Side (SAS) Similarity Statement asserts that if the measures of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.

Side-Angle-Side (SAS)

ÐB @ ÐE

DE = (x)AB

EF = (x)BC

Side-Side-Side (SSS) The Side-Side-Side (SSS) Similarity

Statement asserts that if the measures of the

corresponding sides of two triangles are

proportional, then the triangles are similar.

Side-Side-Side (SSS)

DE = (x)AB

EF = (x)BC

DF = (x)AC

Proofs • A proof is a set of justified statements organized to

form a convincing argument that a given statement is true.

• Definitions, algebraic properties, and previously proven statements can be used to prove a given statement.

• There are several types of proofs, such as paragraph proofs, two-column proofs, and flow diagrams.

• In other words, proofs are just like solving but includes an explanation of what you did.

Example 1 (pg. 197)

Example 2 (pg. 198) Determine whether the triangles are similar. Write a similarity statment.

Example 3 (pg. 198) Determine whether the triangles are similar. Write a similarity statement.

Example 4 (pg. 198)

Triangle Proportionality Theorem

Example 1 (pg. 209)

Example 2 (pg. 210)

Triangle Proportionality Theorem

Example 3 (pg. 210)

Example 4 (pg. 211) Is ?

Triangle Angle Bisector Theorem

ÐABD @ ÐDBC

AD

DC=

BA

BCtherefore

Example 5 (pg. 211) Let’s just look at how we would set this up.

Assignment

• WB Pg 201 #’s 1-10

(On #’s 8-10, assume the given triangles are similar)

• WB Pg 215 #’s 1-10