Question

Are the following triangles similar by the angle-

angle similarity theorem?
A.No, the triangles don't have three angles.
B.Yes, one of the triangles is smaller than
the other.
C.Yes, two pairs of congruent angles are
marked.
D.No, the triangles don't share two pairs of
congruent angles.

Answer 1

D. No, the triangles don't share two pairs of congruent angles.

Explanation:

Two triangles can only be proven similar from the AA (Angle-Angle) similarity theorem if it can be deduced that they share two congruent angles.

In this case, both triangles share one angle, however no other angles can be deduced to be congruent. Therefore, the triangles cannot be proven similar from the AA similarity theorem because they do not share two pairs of congruent angles (corresponds with answer choice D).

Answer 2

D.No, the triangles don't share two pairs of congruent angles.

Explanation:

We know that angle M equals angle H and that angle I equals the unmarked angle.

We do not know that angle N equals angle O so we cannot state that the triangles are similar