Unit 7 Lesson 3 Proving Triangles Similar

Unit 7 Lesson 3: Proving Triangles Similar

Lesson Overview

Proving Triangles Similar

What You Will Learn

determining when two triangles are similar using the relationships among the three pairs of corresponding angles

Overview

In this lesson, you will learn how to determine whether two triangles are similar.

Essential Understanding

You can show that two triangles are similar when you know the relationships between only two or three pairs of corresponding parts. Sometimes, using a ruler or other measuring device, you can use similar triangles to find lengths that cannot be measured easily. You can use indirect measurement to find lengths that are difficult to measure directly. One indirect measurement method uses the fact that light reflects off a mirror at the same angle at which it hits the mirror.

This course is based on a textbook that is viewable by clicking on the textbook icon. Keep the textbook open while you go through the lesson so that you may refer to it throughout the lesson.

Lesson 3: Proving Triangles Similar

Resource Videos

Proving Triangle Similar

Proving Triangle Similar (SSS, SAS, AA)

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Prepare for Application

Instructions

You have now studied Proving Triangles Similar. It is now time to demonstrate your learning.

Try the activities below on your own. You should be able to answer these before beginning the practice.

Create a journal entry called 'Unit 7: Lesson 3 activities' and do these activities in your journal.

Activity 1

Are the two triangles similar? How do you know?

1.
Activity 1

2. Activity 1

Activity 2

Are the triangles similar? If so, write a similarity statement for the triangles and explain how you know the triangles are similar.

1. Activity 2

2. Activity 2

Activity 3

Given: $\bar{M P} ∥ \bar{A C}$

Prove: $△ A B C ~ △ P B M$

For the figure in question 1, suppose you are given only that $\frac{C A}{P M} = \frac{C B}{M B}$ . Could you prove that the triangles are similar? Explain.

Activity 3

Activity 4

Refer to Problem 4 on page 454 of your textbook. Why must the ground be flat to use the indirect measurement method illustrated? Explain.

Unit 7 Lesson 3 Proving Triangles Similar

Unit 7 Lesson 3: Proving Triangles Similar

Prepare for Application

For the figure in question 1, suppose you are given only that CAPM=CBMB. Could you prove that the triangles are similar? Explain.

For the figure in question 1, suppose you are given only that $\frac{C A}{P M} = \frac{C B}{M B}$ . Could you prove that the triangles are similar? Explain.