Question

Are the two triangles similar? How do you know?

A.No
B.Yes AA~
C.Yes SAS
D.Yes SSS

Answer 1

Option(B) is correct.

ΔHMG ≅ ΔKMJ ( by AA similarity criteria )

Explanation:

Vertically opposite angle are two opposite angle formed when two lines cross each other.

Consider the two triangles ΔHMG and ΔJMK

∠MHG = ∠JKM = 47° (given)

also, ∠JMK = ∠HMG (vertically opposite angles)

Thus, ΔHMG ≅ ΔKMJ ( by AA similarity criteria )

AA similarity - if two angles of a triangles are equal to two triangle of another triangle then the two triangles are said to be similar.

Also note that if two angles of a triangle are equal then it is necessary that third angle is also equal.

Hence, Option(B) is correct.

Answer 2

If we solve for the angles in the given figure above, we can note that the corresponding angles are congruent. The triangles can be similar using the AAA, meaning all of its corresponding angles are congruent. Thus, for this item, the triangles are similar. The answer is letter B.