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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 21 Page 608

Begin by identifying the pairs of congruent angles, then compare the ratios of corresponding sides.

Are the Triangles Similar? No.
Explanantion: See solution.

Practice makes perfect

To determine whether two polygons are similar, we need to follow two steps.

Identify pairs of congruent angles.
Compare the ratios of corresponding sides.

Let's analyze the given polygons.

We can find the unknown measures of the angles ∠ N and ∠ O by using the Interior Angles Theorem. Let's start with △ LMN.

m∠ L+ m∠ M + m∠ N = 180 °

m∠ L= 42 °, m∠ M= 90 °

42 ° + 90 ° + m∠ N = 180 °

▼

Solve for m ∠ N

Add terms

132 ° + m ∠ N = 180 °

LHS-132 °=RHS-132 °

m ∠ N = 48 °

We will apply the same process to △ OPQ to solve for ∠ O.

m∠ O + m∠ P + m∠ Q = 180 °

m∠ P= 90 °, m∠ Q= 58 °

m∠ O + 90 ° + 58 ° = 180 °

▼

Solve for m ∠ O

Add terms

m ∠ O + 148 ° = 180 °

LHS-148 °=RHS-148 °

m ∠ O = 32 °

Let's add this new information to the graph.

Because the angle measures in △ LMN are 90 °, 48 °, and 42 °, while the angle measures in △ OPQ are 90 °, 58 °, and 32 °, we can tell that the angles are not all congruent. Therefore, the given polygons are not similar.

Subchapter links

1 Ratios and Proportions p.607

2 Similar Polygons p.607

3 Similar Triangles p.608

4 Parallel Lines and Proportional Parts p.608

5 Parts of Similar Triangles p.609

6 Similarity Transformations p.609

7 Scale Drawings and Models p.610