What ADDITIONAL information is needed to prove that △ABC≅△EDC

Question

What ADDITIONAL information is needed to prove that △ABC≅△EDC
 using SAS if point C is the midpoint of both BD¯¯¯¯¯¯¯¯  and AE¯¯¯¯¯¯¯¯

(1 point)
Responses

∠ACB≅∠ECD
∠ACB≅∠ECD

BD¯¯¯¯¯¯¯¯≅ DC¯¯¯¯¯¯¯¯
BD¯¯¯¯¯¯¯¯≅ DC¯¯¯¯¯¯¯¯

AB¯¯¯¯¯¯¯¯≅ ED¯¯¯¯¯¯¯¯
AB¯¯¯¯¯¯¯¯≅ ED¯¯¯¯¯¯¯¯

∠BAC≅∠DEC
∠BAC≅∠DEC
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GPT-4o mini · Answer

To prove that triangles $ \triangle ABC \cong \triangle EDC $ using the Side-Angle-Side (SAS) criterion, we need to establish that two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle. Since it is given that point $ C $ is the midpoint of both $ \overline{BD} $ and $ \overline{AE} $, we can infer that: 1. $ \overline{BC} \cong \overline{DC} $ (because $ C $ is the midpoint of $ \overline{BD} $) 2. $ \overline{AC} \cong \overline{EC} $ (because $ C $ is the midpoint of $ \overline{AE} $) We also need to show that the included angles are congruent to use the SAS criterion. Therefore, the additional information needed to prove $ \triangle ABC \cong \triangle EDC $ using the SAS criterion is: $$ \angle ACB \cong \angle ECD $$ This option establishes that the included angles between the congruent sides are equal, forming the SAS relationship needed for triangle congruence.