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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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Answers
GPT-4o mini
To use the Side-Angle-Side (SAS) postulate to prove that triangles \( \triangle ABC \) and \( \triangle EDC \) are congruent, you need to show that two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle.
Since point C is the midpoint of both \( \overline{BD} \) and \( \overline{AE} \), it implies that:
- \( \overline{BC} \) is congruent to \( \overline{DC} \) (because \( C \) is the midpoint of \( \overline{BD} \))
- \( \overline{AC} \) is congruent to \( \overline{CE} \) (because \( C \) is the midpoint of \( \overline{AE} \))
Thus, if you have \( \overline{AC} \) and \( \overline{CE} \) congruent, and you also need the angle \( \angle ACB \) to be congruent to \( \angle ECD \), you would choose:
**∠ACB ≅ ∠ECD**
Therefore, the correct response is:
**∠ACB ≅ ∠ECD**
Since point C is the midpoint of both \( \overline{BD} \) and \( \overline{AE} \), it implies that:
- \( \overline{BC} \) is congruent to \( \overline{DC} \) (because \( C \) is the midpoint of \( \overline{BD} \))
- \( \overline{AC} \) is congruent to \( \overline{CE} \) (because \( C \) is the midpoint of \( \overline{AE} \))
Thus, if you have \( \overline{AC} \) and \( \overline{CE} \) congruent, and you also need the angle \( \angle ACB \) to be congruent to \( \angle ECD \), you would choose:
**∠ACB ≅ ∠ECD**
Therefore, the correct response is:
**∠ACB ≅ ∠ECD**