Question

Are the two triangles below similar? (My guess is C)

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

Answer 1

Both triangles have identical inside angles, so the answer should be::

B: Yes, because there are two pairs of congruent corresponding angles

Answer 2

Answer: B: Yes, because there are two pairs of congruent corresponding angles.

Step-by-step explanation:

In ΔTUV

∠T+∠U+∠V=180° [By angle sum property of triangle]

⇒ ∠T= 180°-∠V-∠U

⇒ ∠T= 180°-55°-80°

⇒∠T=180°-135°

⇒∠T=45°

Now, in ΔTUV and ΔXYW

∠T=∠X=45° and ∠V=∠W=55°

⇒ ΔTUV ≈ ΔXYW  [AA- similarity criteria of triangles.]

AA Similarity Postulate tells that two triangles are said to be similar if they have two corresponding angles that are congruent in measure.