Question

Which postulate or theorem proves that △CFE and △DFE are congruent?



​ HL Congruence Theorem ​

SSS Congruence Postulate

​ AAS Congruence Theorem ​

​ SAS Congruence Postulate ​

Answer 1

The correct answer is:

SAS

Explanation:

In the diagram, we have that CE and ED are congruent.

We also know that ∠FEC≅∠FED; this is because these two angles form a linear pair.  A linear pair has a sum of 180°; since m∠FED = 90°, this means that m∠FEC = 180-90 = 90°, and the two angles are congruent.

We also know that FE = FE, due to the reflexive property.

This gives us two sides and the angle between them, or SAS.