See Problem 3.

13. Proof Given: ∠ A B C ≅ ∠ A C D angle eh b c approximately equal to angle eh c d

    Prove: △ A B C ∼ △ A C D white up pointing triangle eh b c , tilde operator white up pointing triangle eh c d

    
14. Proof Given: P R = 2 N P , P Q = 2 M P table with 2 rows and 3 columns , row1 column 1 , p r , column 2 equals , column 3 2 n p comma , row2 column 1 , p q , column 2 equals , column 3 2 m p , end table

    Prove: △ M N P ∼ △ Q R P white up pointing triangle m n p , tilde operator white up pointing triangle q r p

    

See Problem 4.

Indirect Measurement Explain why the triangles are similar. Then find the distance represented by x.

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17. Washington Monument At a certain time of day, a 1.8-m-tall person standing next to the Washington Monument casts a 0.7-m shadow. At the same time, the Washington Monument casts a 65.8-m shadow. How tall is the Washington Monument?

B Apply

Can you conclude that the triangles are similar? If so, state the postulate or theorem you used and write a similarity statement. If not, explain.

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21. 1. Are two isosceles triangles always similar? Explain.
    2. Are two right isosceles triangles always similar? Explain.
22. Think About a Plan On a sunny day, a classmate uses indirect measurement to find the height of a building. The building's shadow is 12 ft long and your classmate's shadow is 4 ft long. If your classmate is 5 ft tall, what is the height of the building?
    • Can you draw and label a diagram to represent the situation?
    • What proportion can you use to solve the problem?
23. Indirect Measurement A 2-ft vertical post casts a 16-in. shadow at the same time a nearby cell phone tower casts a 120-ft shadow. How tall is the cell phone tower?

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