If point C

Question

is the midpoint of both BD¯¯¯¯¯¯¯¯
and AE¯¯¯¯¯¯¯¯
, what additional information would you need to be able to state that △ABC≅△EDC
by the SSS Congruence Theorem?

BC¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯
line segment cap b cap c is congruent to line segment cap d cap c - no response given

AE¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯
line segment cap A cap e is congruent to line segment cap d cap b - no response given

AB¯¯¯¯¯¯¯¯≅ED¯¯¯¯¯¯¯¯
line segment cap A cap b is congruent to line segment cap e cap d - no response given

∠ACB≅∠ECD

Answer 1

To apply the SSS (Side-Side-Side) Congruence Theorem to show that triangles \( \triangle ABC \) and \( \triangle EDC \) are congruent, you would need to establish that all three pairs of corresponding sides of the triangles are congruent.

1. Given Information:

   • Point \( C \) is the midpoint of \( \overline{BD} \) and \( \overline{AE} \), which means \( \overline{BC} \cong \overline{DC} \) and \( \overline{AC} \cong \overline{EC} \).

2. Required Information:

   • You need to demonstrate that \( \overline{AB} \cong \overline{ED} \).

3. Conclusion:

   • If you can show that \( \overline{AB} \cong \overline{ED} \) in addition to the information that \( \overline{BC} \cong \overline{DC} \) (from the midpoint property) and \( \overline{AC} \cong \overline{EC} \) (also from the midpoint property), then you can conclude that \( \triangle ABC \cong \triangle EDC \) by the SSS Congruence Theorem.

Thus, the additional information needed is:

\( \overline{AB} \cong \overline{ED} \).