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**3.4: Using Similar Triangles**

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**Angles of Similar Triangles**

When two angles in one triangle are congruent to two angles in another triangle, the third angles are also congruent and the triangles are similar. Indirect Measurement uses similar triangles to find a missing measure when it is difficult to find directly.

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**Identifying Similar Triangles**

Tell whether the triangles are similar explain. The triangles have two pairs of congruent angles. So, the third angles are congruent, and the triangles are similar.

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**Identifying Similar Triangles**

Tell whether the triangles are similar. Explain. Write and solve an equation to find x. Write and solve an equation to find x. The triangles have two pairs of congruent angles. So, the third are congruent and the triangles are similar. The triangles do not have two pairs of congruent angles. So, the triangles are not similar.

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**Practice Tell whether the triangles are similar. Explain**

Solve the equation for x. Solve the equation for x. The triangles do not have two pairs of congruent angles. So, the triangles are not similar. The triangles have two pairs of congruent angles. So, the third are congruent and the triangles are similar.

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**Using Indirect Measurement**

You plan to cross a river and want to know how far it is to the other side. You take measurements on your side of the river and make the drawing shown. (a) Explain why ABC and DEC are similar. (b) What is the distance x across the river? a) <B and <E are right angles, so they are congruent. <ACB and <DCE are vertical angles, so they are congruent. Because two angles in ABC are congruent to two angles in DEC, the third angles are also congruent and the triangles are similar. b) The ratios of the corresponding side lengths in similar triangles are equal. Write and solve a proportion to find x. So the distance across the river is 48 feet.

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