Question

Are the two triangles below similar?

Triangles MNO and PRQ are shown. Angle N measures 105 degrees, angle O measures 50 degrees, side MN measures 15, side NO measures 9, angle P measures 50 degrees, angle Q measures 25 degrees, side QR measures 5, side PR measures 3.

A. No, because the corresponding sides are not proportional
B. Yes, because the corresponding sides are proportional
C. No, because there are not two pairs of congruent corresponding angles
D. Yes, because there are two pairs of congruent corresponding angles

Answer 1

The answer is Yes, because there are two pair of congruent corresponding angles.

Answer 2

Answer: D. Yes, because there are two pairs of congruent corresponding angles,∠M=∠Q=25° and ∠O=∠P=50°.

Explanation:

Given: ΔMNO with NO=9 , ∠N=105° and ∠O=50° then by angle sum property of triangles

∠M+∠N+∠O=180°

⇒∠M=180°-(∠N+∠O)

⇒∠M=180°-(105°+50°)

⇒∠M=180°-(155°)

⇒∠M=25°

Now in ΔMNO and ΔPRQ

∠M=∠Q=25° and ∠O=∠P=50°

Therefore by AA similarity criteria for similar triangles ,they are similar

i.e. ΔMNO ≈ ΔPRQ.

Thus D is the right option.