Question

If point C is the midpoint of both BD¯¯¯¯¯¯¯¯ and AE¯¯¯¯¯¯¯¯ , what additional information would you need to be able to state that △ABC≅△EDC by the SAS Congruence Theorem? (1 point) Responses ∠ACB≅∠ECD angle upper A upper C upper B congruent to angle upper E upper C upper D ∠A≅∠E angle upper A congruent to angle upper E BC¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ Modifying above upper B upper C with bar congruent to Modifying above upper D upper C with bar AB¯¯¯¯¯¯¯¯≅ED¯¯¯¯¯¯

Answer 1

To use the SAS (Side-Angle-Side) Congruence Theorem to establish that △ABC ≅ △EDC, you need to show that:

1. Two sides of one triangle are congruent to two sides of the other triangle.
2. The angle between those two sides in one triangle is congruent to the angle between the corresponding two sides in the other triangle.

Given that point C is the midpoint of both segments \( BD \) and \( AE \), we have:

- \( BC \) is congruent to \( DC \).
- \( AC \) is congruent to \( EC \).

Thus, you just need to establish the congruence of the angle ∠ACB and ∠ECD.

From the options provided, to meet the condition for SAS, the necessary additional information you would need is:

**∠ACB ≅ ∠ECD** (This establishes that the included angle between sides AC and BC in triangle ABC is congruent to the included angle between sides EC and DC in triangle EDC.)

So, the response is:

**∠ACB ≅ ∠ECD**.