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Unit 2 - Lesson 8 - Grade 8: Illustrative Mathematics

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Grade 8 Unit 2
Lesson 8: Similar Triangles
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 2
Lesson 8: Similar Triangles
CC BY 2021 Illustrative Mathematics®
Lesson: Similar Triangles

Equivalent Expressions (Warm Up)

1.

Create three different expressions that are each equal to 20. Each expression should include only these three numbers: 4, -2, and 10.


Making Pasta Angles and Triangles

Your teacher will give you some dried pasta and a set of angles.

Create a triangle using three pieces of pasta and angle A. 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.
2.

After you have created your triangle, measure each side length with a ruler and record the length. Then measure the angles to the nearest 5 degrees using a protractor and record these measurements.


3.

Find two others in the room who have the same angle A and compare your triangles. What is the same? What is different? Are the triangles congruent? Similar?


4.

How did you decide if they were or were not congruent or similar?

Now use more pasta and angles A, B, and C to create another triangle. Tape this pasta triangle on a separate sheet of paper.



b. Find two others in the room who used your same angles and compare your triangles.
5.

After you have created your triangle, measure each side length with a ruler and record the lengths. Then measure the angles to the nearest 5 degrees using a protractor and record these measurements.


6.

Find two others in the room who used your same angles and compare your triangles. What is the same? What is different? Are the triangles congruent? Similar?


7.

How did you decide if they were or were not congruent or similar?

Here is triangle PQR. Break a new piece of pasta, different in length than segment PQ.
  • Tape the piece of pasta so that it lays on top of line PQ with one end of the pasta at P (if it does not fit on the page, break it further). Label the other end of the piece of pasta S.
  • Tape a full piece of pasta, with one end at S, making an angle congruent to .
  • Tape a full piece of pasta on top of line PR with one end of the pasta at P. Call the point where the two full pieces of pasta meet T.
8.

Is your new pasta triangle PST similar to ΔPQR ? Explain your reasoning.

9.

If your broken piece of pasta were a different length, would the pasta triangle still be similar to ΔPQR? Explain your reasoning.

Similar Figures in a Regular Pentagon (Optional)

This diagram has several triangles that are similar to triangle DJI.
10.

Three different scale factors were used to make triangles similar to DJI. In the diagram, find at least one triangle of each size that is similar to DJI.

11.

Explain how you know each of these three triangles is similar to DJI.

12.

Find a triangle in the diagram that is not similar to DJI.

Cool Down: Applying Angle-Angle Similarity

Applying Angle-Angle Similarity

Here are two triangles.
13.

Show that the triangles are similar.

14.

What is the scale factor from triangle ABC to triangle A'B'C'?