Question

which postulate or theorem proves that △cfe and △dfe are congruent? hl congruence theorem sas congruence postulate sss congruence postulate aas congruence theorem

Explanation:

Step1: Analyze the given triangles

We have two right - angled triangles \(\triangle CFE\) and \(\triangle DFE\). The right angles are at \(E\). We know that \(CE = DE\) (given by the equal segment marks), \(FE=FE\) (common side).

Step2: Recall the HL Congruence Theorem

The HL (Hypotenuse - Leg) Congruence Theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent. In \(\triangle CFE\) and \(\triangle DFE\), \(CF\) and \(DF\) are hypotenuses, \(CE\) and \(DE\) are legs, and \(FE\) is common.

Answer:

HL Congruence Theorem