Question

If point C is the midpoint of both BD¯¯¯¯¯¯¯¯BD¯ and AE¯¯¯¯¯¯¯¯AE¯ , what additional information would you need to be able to state that △ABC≅△EDC by the SSS Congruence Theorem?
(1 point)
¯¯AE¯≅DB¯
¯¯¯BC¯≅DC¯
∠ACB≅∠ECD
¯¯¯AB¯≅ED¯

Answer 1

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

Given that point C is the midpoint of segments \(\overline{BD}\) and \(\overline{AE}\), you have established that:

- \(\overline{BC} \cong \overline{DC}\) (since C is the midpoint of \(\overline{BD}\))
- \(\overline{AC} \cong \overline{EC}\) (since C is the midpoint of \(\overline{AE}\))

To use the SSS theorem, you need one additional piece of information that would allow you to equate the third sides of the triangles:

- You need to know that \(\overline{AB} \cong \overline{ED}\).

Thus, the correct additional information to conclude that \(\triangle ABC \cong \triangle EDC\) by the SSS Congruence Theorem is:

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