Question

Are the two triangles below similar?

Answer 1

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

Step-by-step 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.

Answer 2

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