To determine which theorem proves that triangle \( \triangle ABC \) is congruent to triangle \( \triangle ABD \), we need to know the information provided in the picture. However, based on the options given, here are brief explanations of the relevant triangle congruence theorems:
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HL Theorem: This states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
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SSS Theorem: This stands for Side-Side-Side, which states that if all three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.
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SAS Theorem: This stands for Side-Angle-Side, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
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ASA Theorem: This stands for Angle-Side-Angle, which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Given the congruence statement \( \triangle ABC \cong \triangle ABD \) and without additional details, you will need to refer to the specific information provided in the picture to choose the correct theorem.
If both triangles share side \( AB \), and you have at least one pair of congruent angles and the shared side, you might use ASA. If you are given two sides and the included angle, SAS would be applicable. For congruence based on sides alone, you would use SSS, and if you are dealing with right triangles, the HL theorem could be applicable.
Please provide more context or details from the picture to arrive at the correct conclusion.
1 answer