Question

AC ≅ AE; ∠ACD ≅ ∠AED Triangles A C F and A E B overlap. Point F of triangle A C F is on side A E of triangle A E B. Point B of triangle A E B is on side A C of triangle A C F. The triangles intersect to form point D. Which relationships within the diagram are true? Check all that apply. △ACF ≅ △AEB because of ASA. △ACF ≅ △AEB because of SAS. △ACF ≅ △AEB because of AAS. ∠CFA ≅ ∠EBA FC ≅ BE FC ≅ AC

Answer 1

Answer: its 1,4 and 5 .

Explanation:

1 △ACF ≅ △AEB because of ASA.

2 △ACF ≅ △AEB because of SAS.

3 △ACF ≅ △AEB because of AAS.

4 ∠CFA ≅ ∠EBA

5 FC ≅ BE

6 FC ≅ AC

Answer 2

Triangles ACF and AEB are congruent because AC is congruent to AE and angle ACD is congruent to angle AED.

Step-by-step explanation:

To determine the relationships within the diagram, we need to analyze the given information about the triangles. We are given that AC is congruent to AE and that angle ACD is congruent to angle AED. Based on these congruences, we can conclude that triangles ACF and AEB are congruent. However, we cannot use ASA, SAS, or AAS to prove this congruence. Therefore, the correct relationship is: △ACF ≅ △AEB because of AC ≅ AE and ∠ACD ≅ ∠AED.

Additionally, we can determine that ∠CFA is congruent to ∠EBA since these angles are corresponding angles formed by parallel lines AC and BE. However, we cannot determine if FC is congruent to BE or if FC is congruent to AC based on the given information.