Lesson 8.2 Proving Triangle Similarity by AA Learning Target: Understand and use the Angle-Angle Similarity Theorem. Success Criteria: I can use similarity transformations to prove the Angle-Angle Similarity Theorem. I can use angle
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Presentation Transcript
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Lesson 8.2 Proving Triangle Similarity by AA<br>
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Learning Target:
Understand and use the Angle-Angle Similarity Theorem. Success Criteria:
I can use similarity transformations to prove the Angle-Angle Similarity Theorem.
I can use angle measures of triangles to determine whether triangles are similar.
I can prove triangle similarity using the Angle-Angle Similarity Theorem.
I can solve real-life problems using similar triangles.<br>
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Using the Angle-Angle Similarity Theorem<br>
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Angle-Angle (AA) Similarity Theorem<br>
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Angle-Angle (AA) Similarity Theorem<br>
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Example 1 Using the AA Similarity Theorem Determine whether the triangles are
similar. If they are, write a similarity
statement. Explain your reasoning. SOLUTION READING<br>
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Example 2 Using the AA Similarity Theorem Show that the two triangles are similar and write a similarity statement. SOLUTION<br>
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Solving Real-Life Problems
Previously, you learned a way to use congruent triangles to find measurements indirectly. Another useful way to find measurements indirectly is by using similar triangles.<br>
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Example 3 Modeling Real Life A free-fall ride casts a shadow that is 175 feet long. At the same time, a person standing nearby who is 5 feet 5 inches tall casts a shadow that is 34 inches long. How tall is the free-fall ride? 1. Understand the Problem You are given the length of the shadow of the ride, the height of the person, and the length of the shadow of the person. You need to find the height of the ride. 2. Make a Plan The Sun’s rays hit the ride and the person at the same angle. There are two pairs of congruent angles, so the triangles are similar by the AA Similarity Theorem. Use similar triangles to write and solve a proportion. SOLUTION<br>
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Example 3 Modeling Real Life 3. Solve and Check The ride and the person form sides of two right triangles with their shadows on the ground. You can use a proportion to find the height x. Write 5 feet 5 inches as 65 inches so that you can form two ratios of feet to inches. Write proportion of side lengths. Multiply each side by 65. Divide. The problem asks for the height of the ride. Because your answer is 335 feet, the units are appropriate.<br>
