Unit 2, Lesson 8

Similar Triangles

Grade 8

8.1

Warm-up

A Star and a Pentagon

<p>A pentagon, E D C B A. Points connected by line E J I C, line E F G B, line D J F A, line D I H B, line C H G A forming pentagon J I H G F.</p><br>

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8.2

Activity

Making Pasta Angles and Triangles

Your teacher will give you dried pasta, a set of 3 angles labeled , , and , blank paper, and tape.

Create a triangle using 3 pieces of pasta and angle . Your triangle must include the angle you were given, but you are otherwise free to make any triangle you like. Tape your pasta triangle to a sheet of paper so it won’t move.
1. After you have created your triangle, measure each side length with a ruler and record the length on the paper next to the side. Then measure the angles to the nearest using a protractor and record these measurements on your paper.
2. Find 2 others in the room who have the same angle and compare your triangles. What is the same? What is different?
3. Are the triangles congruent? Are the triangles similar? Explain your reasoning.
Now use more pasta and all 3 angles , , and to create 1 new triangle. Tape this pasta triangle on a separate blank sheet of paper.
1. After you have created your triangle, measure each side length with a ruler and record the length on the paper next to the side. Then measure the angles to the nearest using a protractor and record these measurements on your paper.
2. Find 2 others in the room who used your same 3 angles and compare your triangles. What is the same? What is different?
3. Are the triangles congruent? Are the triangles similar? Explain your reasoning.

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8.3

Activity

Similar Figures in a Regular Pentagon

This diagram has several triangles that are similar to triangle .
1. Three different scale factors were used to make triangles similar to . In the diagram, find at least 1 triangle of each size that is similar to .
2. Explain how you know each of these 3 triangles is similar to .
Find a triangle in the diagram that is not similar to .

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Student Lesson Summary

Two polygons are similar when there is a sequence of translations, rotations, reflections, and dilations taking one polygon to the other. When the polygons are triangles, we only need to check that both triangles have two corresponding angles to show they are similar.

For example, triangle and triangle both have a 30-degree angle and a 45-degree angle.

<p>Two triangles. First, A, B C. Angle A, 30 degrees, angle C, 45 degrees. Second, D, E, F. Angle D, 30 degrees, angle F, 45 degrees.</p><br>

We can translate to and then rotate around point so that the two 30-degree angles are aligned, giving this picture:

Then a dilation with center

and appropriate scale factor will move

to

. This dilation also moves

to

, showing that triangles

and

are similar.

Glossary

None

Practice

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Similar Triangles

Warm-up

A Star and a Pentagon

Are You Ready for More?

Making Pasta Angles and Triangles

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Activity

Similar Figures in a Regular Pentagon

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Student Lesson Summary

Glossary