Exercise 11 Page 455

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

1. AA (Angle-Angle) ~ Postulate: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
2. SSS (Side-Side-Side) ~ Theorem: If the corresponding side lengths of two triangles are proportional, then the triangles are similar.
3. SAS (Side-Angle-Side) ~ 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.

We know the measures of two of the angles of △ NUS. To find the measure of the third angle, we can create an equation using the Triangle Angle Sum Theorem. 35 + 25 + m ∠ U =180 Let's solve this equation for the measure of the missing angle.

35 + 25 + m ∠ U =180

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Solve for m ∠ U

AddTerms

Add terms

60 + m ∠ U = 180

SubEqn

LHS-60=RHS-60

m ∠ U =120

The measure of ∠ U is 120 ^(∘). We also know the measures of two of the angles of △ ARY. To find the measure of the third angle, we can create an equation using the Triangle Angle Sum Theorem once more. 35 + 110 + m ∠ R =180 Let's solve this equation for the measure of the missing angle.

35 + 110 + m ∠ R =180

▼

Solve for m ∠ R

AddTerms

Add terms

145 + m ∠ R = 180

SubEqn

LHS-145=RHS-145

m ∠ R = 35

The measure of ∠ R is 35 ^(∘).

Only one pair of angles is congruent. Because not all of the corresponding angles are congruent, the triangles are not similar.