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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.

ANo, because the corresponding sides are not proportional
BYes, because the corresponding sides are proportional
CNo, because there are not two pairs of congruent corresponding angles
DYes, because there are two pairs of congruent corresponding angles

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 me class=

Verified Answer :

Student118

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

JeanaShupp

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.


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