Question

Given:

CF = DF


Prove:
1 = 2

Based on the given information, which of the following lines would be in this proof?
Triangle FCE congruent to Triangle FDE by HL.
Triangle FCE congruent to Triangle FDE by LA.
Triangle ACF congruent to Triangle BDF by HL.

Answer 1

Triangle FCE congruent to Triangle FDE by HL. I thought at first that it was answer 2, but after further study it is answer 1

Answer 2

ΔFCE≅ΔFDE

Explanation:

Given: CF=DF

In ΔFCE and ΔFDE,

CF=DF (Given)

∠CFE=∠DFE (Equal sides have equal angles)

FE=FE (common)

Therefore, by SAS rule of congruency,

ΔFCE≅ΔFDE,

⇒∠1=∠2

Hence option A is used in solving the problem.