Exercise 1 Page 557

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

From the picture, we can see that the angles

Q

and

V

have the same measure. This means that they are congruent angles.

∠ Q ≅ ∠ V

Now, we have to find the measure of the third angle in either of the two triangles to determine whether they are similar. Let's consider triangle

R Q S .

We know that the sum of the measures of the interior of a triangle is always

18 0^{\circ} .

This lets us write an equation to find

m ∠ R .

47 + 68 + m ∠ R = 180

Let's solve this equation for

m ∠ R .

47 + 68 + m ∠ R = 180

▼

Solve for

m ∠ R

AddTerms

Add terms

115 + m ∠ R = 180

SubEqn

$LHS - 115 = RHS - 115$

115 + m ∠ R - 115 = 180 - 115

SubTerms

Subtract terms

m ∠ R = 65

The measure of

∠ R

is

6 5^{\circ} .

Let's mark it on the picture.

We can see that only one pair of angles is congruent. This means that by the rule for Angle-Angle (AA) Similarity these triangles are not similar.