Question

Suppose that m∠A = m∠D. Which other fact would guarantee that the triangles are SIMILAR?

A)
AB
__
DE
=
CB
__
FE

B) m∠C = m∠F

C) m∠A + m∠B + m∠C = 180°

D) 180° - m∠D = m∠E + m∠F

Answer 1

B) m∠C = m∠F
Because now m∠B = m∠E because of the 180 total rule, and if all 3 ∠s are = then they are similar

Answer 2

Answer: B) m∠C = m∠F

Explanation:

Given: In triangles ΔABC and Δ DEF

m∠A = m∠D

To prove both the triangles are similar, we need at-least one one information which is given in option B.

If m∠C = m∠F , then AA similarity criteria , ΔABC and Δ DEF are similar.

If we choose A) then it will not follow SAS criteria of similarity because ∠A and ∠D are not included angles of AB, CB and DE, FE respectively.

SAS similarity criteria for similar triangles says that if two sides of a triangle are proportional to two sides of another triangle and their included angles are equal, then the triangles are said to be similar.