Lesson 3.3:Proving Similar TrianglesSECTIONS 5.4.1 AND 5.4.2

PAGES 70-92

Introduction 5.4.1 (page 70)•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

5 2 15

6

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.

Example 1 (pg. 71)

Example 2 (pg. 72)Determine whether the triangles are similar. Write a similarity statment.

Example 3 (pg. 72)Determine whether the triangles are similar. Write a similarity statement.

Example 4 (pg. 72)

Introduction 5.4.2 (page 82)Archaeologists, among others, rely on the Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS) similarity statements to determine actual distances and locations created by similar triangles. Many engineers, surveyors, and designers use these statements along with other properties of similar triangles in their daily work. Having the ability to determine if two triangles are similar allows us to solve many problems where it is necessary to find segment lengths of triangles.

Triangle Proportionality Theorem• Parallel lines are lines in a plane that either do not share

any points and never intersect, or share all points.

• If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the parallel line divides these two sides proportionally.

Triangle Proportionality Theorem

Triangle Proportionality Theorem

Example 1 (pg. 83)

Example 2 (pg. 84)

Example 3 (pg. 84)

Example 4 (pg. 85)Is ?

Triangle Angle Bisector Theorem

ÐABD @ ÐDBC

AD

DC=

BA

BCtherefore

Example 5 (pg. 85)

Assignment

• WB Pg 75 #’s 1-10 (On #’s 8-10, assume the given triangles are similar)

• WB Pg 89 #’s 1-10