Exercise 2 Page 556

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

From the picture, we can see that both triangles are right triangles. This means that their corresponding angles are congruent and have a measure of

9 0^{\circ} .

∠ M ≅ ∠ P

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

L M N .

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 ∠ N .

35 + 90 + m ∠ N = 180

Let's solve this equation for

m ∠ N .

35 + 90 + m ∠ N = 180

▼

Solve for

m ∠ N

AddTerms

Add terms

125 + m ∠ N = 180

SubEqn

$LHS - 125 = RHS - 125$

125 + m ∠ N - 125 = 180 - 125

SubTerms

Subtract terms

m ∠ N = 55

The measure of

∠ N

is

5 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.