Question

which relationships within the diagram are true? check all that apply.
□ fc ≅ ac
□ fc ≅ be
□ ∠cfa ≅ ∠eba
□ △acf ≅ △aeb because of aas.
□ △acf ≅ △aeb because of sas.
□ △acf ≅ △aeb because of asa.
ac ≅ ae; ∠acd ≅ ∠aed

Explanation:

Step1: Recall triangle - congruence postulates

AAS (Angle - Angle - Side) states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, the triangles are congruent. SAS (Side - Angle - Side) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. ASA (Angle - Side - Angle) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

Step2: Analyze the given information

We are given that $\overline{AC}\cong\overline{AE}$ and $\angle ACD\cong\angle AED$. There is no information given about $\overline{FC}\cong\overline{AC}$ or $\overline{FC}\cong\overline{BE}$ or $\angle CFA\cong\angle EBA$.
For $\triangle ACF$ and $\triangle AEB$, we do not have enough information to use AAS, SAS, or ASA to prove congruence.

Answer:

None of the given relationships are true based on the information provided.