H. Geometry 7.3 - Proving Similar Triangles Date: __________

Objective: I can use dilation and rigid motion to establish triangle similarity theorems. I can use AA~, SSS~, and SAS~ to prove triangles are similar.

Do the ‘Explore and Reason/Habits of Mind’ in your Student Companion on page 171.

How does knowing two pairs of angles of two triangles are congruent allow you to show the triangles are similar?

Essential Question: How can you use the _______________ and _______________ of two triangles to determine whether they are _______________?

Example 1: Establish the Angle-Angle Similarity (AA~) Theorem

Do the ‘Try It 1’ in your Student Companion on page 172.

Example 2: Establish the Side-Side-Side Similarity (SSS~) Theorem

Do the ‘Try It 2’ in your Student Companion on page 172.

Theorem 7-1: Angle-Angle Similarity (AA~) Theorem

If two _______________ of one triangle are _______________

to two _______________ of another triangle, then the triangles

are _______________

Example 3: Verify Triangle Similarity

A. Are ∆ ABC∧∆≝¿ similar?

B. Are ∆ PQS∧∆RQP similar?

Do the ‘Try It 3 and Habits of Mind’ in your Student Companion on page 172.

Why is there no ASA~ theorem?

Is it necessary to know the proportions of all three pairs of sides in Part A? In Part B?

Theorem 7-2: Side-Side-Side Similarity (SSS~) Theorem

If the _______________ sides of two triangles are

_______________, then the triangles are _______________.

Theorem 7-3: Side-Angle-Side Similarity (SAS~) Theorem

If an _______________ of one triangle is _______________

to an _______________ of a second triangle, and the sides that

include the two _______________ are _______________, then

the triangles are similar.

Example 4: Find Lengths in Similar Triangles

What is MN?

Could you prove the triangles are congruent using the AA~ theorem?

Do the ‘Try It 4’ in your Student Companion on page 173.

Example 5: Solve Problems Involving Similar Triangles

Do the ‘Try It 5 and Habits of Mind’ in your Student Companion on page 173.HW #9:

1. Student Companion Book:

page 174

problems: 1-9

2. Hard Cover Book:

page: 322

problems: 11, 13, 16-18, 19, 20, 26