Ac ≅ ae; ∠acd ≅ ∠aed ac ≅ ae; ∠acd ≅ ∠aed which relationships within the diagram are true? check all that apply. a) △acf ≅ △aeb because of asa. b) △acf ≅ △aeb because of sas. c) △acf ≅ △aeb because of aas. d) ∠cfa ≅ ∠eba e) fc ≅ be f) fc ≅ ac

Answers:

A) △ACF ≅ △AEB because of ASA.

D) ∠CFA ≅ ∠EBA

E) FC ≅ BE

Solution:

AC ≅ AE; ∠ACD ≅ ∠AED Given

The angle ∠CAF ≅ ∠EAB, because is the same angle in Vertex A

Then △ACF ≅ △AEB because of ASA (Angle Side Angle): They have a congruent side (AC ≅ AE) and the two adjacent angles to this side are congruent too (∠ACD ≅ ∠AED and ∠CAF ≅ ∠EAB), then  option A)  is true: △ACF ≅ △AEB because of ASA.

If the two triangles are congruent, the ∠CFA ≅ ∠EBA; and FC ≅ BE, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), then Options D) ∠CFA ≅ ∠EBA and E) FC ≅ BE are true