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Question

Question
△ABC≅△ABD
Using the info provided in the picture below, which theorem proves this?

(1 point)
Responses

ASA Theorem
ASA Theorem

HL Theorem
HL Theorem

SAS Theorem
SAS Theorem

SSS Theorem

Answer 1

To determine which theorem can be used to prove that triangles \( \triangle ABC \) and \( \triangle ABD \) are congruent (as indicated by \( \triangle ABC \cong \triangle ABD \)), we would need to provide information about the sides and angles of both triangles.

Here are the meanings of each theorem:

1. ASA Theorem (Angle-Side-Angle): Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

2. HL Theorem (Hypotenuse-Leg): This applies specifically to right triangles. It states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

3. SAS Theorem (Side-Angle-Side): Two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

4. SSS Theorem (Side-Side-Side): Two triangles are congruent if all three sides of one triangle are equal to all three sides of another triangle.

Based on congruence notations and the information given, if triangles \( \triangle ABC \) and \( \triangle ABD \) have two sides and the included angle equal, then SAS would be the correct choice if sides \( AB \) and \( AC \) and the angle at \( A \) are congruent.

If you have specific measurements or angles from the picture mentioned, please provide them for further assistance in selecting the correct theorem.