Concept Byte: Right Triangle Ratios

Use With Lesson 10-6

ACTIVITY

In this activity you will explore the ratios of side lengths of similar right triangles.

Activity 1

1. Measure the sides of the right triangles below to the nearest tenth of a centimeter.

   
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2. Copy and complete the table using the side lengths you found in Exercise 1.

   
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3. Reasoning How do the corresponding ratios in the three triangles compare? Will all right triangles with a 65 ° 65 degrees  angle have the same ratios? Explain your reasoning.

Activity 2

4. A right triangle has a 65 ° 65 degrees  angle, and its shortest side is 5 cm long. Predict the lengths of the other two sides.
5. Draw the triangle described in Exercise 4. Measure its sides.
6. How do your measurements compare to your predictions? Were there inaccuracies in your predictions, in the construction of the triangle, or in your measurements? Explain.

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