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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

Mid-Chapter Quiz

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Exercise 11 Page 459

Compare the ratios of the triangles.

Are the Triangles Similar? Yes.
Similarity Statement: △ LMO ~ △ NOM
Explanation: See solution.

Practice makes perfect

Let's review the theorems that can help us prove that two triangles are similar.

Angle-Angle Similarity Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Side-Side-Side Similarity Theorem: If the corresponding side lengths of two triangles are proportional, then the triangles are similar.
Side-Angle-Side Similarity Theorem: If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.

We are asked to determine whether the given triangles are similar.

As we can see in the diagram both triangles form the rectangle LMNO. From here we can deduce that ∠ L ≅ ∠ N, LM ≅ ON, LO ≅ MN, and MO≅ MO. Let's calculate the ratio between LM and ON, between LO and MN, and between MO and MO. Recall that in a rectangle, opposite sides have the same length. LM/ON = 1, LO/MN = 1, and MO/MO=1 As we can see, the ratios are equal. Therefore, the corresponding sides are proportional. By the Side-Side-Side Similarity Theorem, the given triangles are similar. △ LMO ~ △ NOM