Ask a New Question
Menu

NOTE: On the bottom right corner of each question, you will see a button that says “Check Answer.” Click this to check your answer before submitting. It will not tell you the correct answer, but it will tell you whether the answer you selected is correct or not. You can use this feature ONCE per question (only for Quizzes and Sample Works). What theorem could be used to prove that △ABC≅△FED ? (1 point) Responses HL Congruence Theorem HL Congruence Theorem SAS Congruence Theorem SAS Congruence Theorem AAS Congruence Theorem AAS Congruence Theorem ASA Congruence Theorem ASA Congruence Theorem Skip to navigation

1 answer

To determine which theorem could be used to prove that triangle \( \triangle ABC \) is congruent to triangle \( \triangle FED \), we would need to consider what information is given about the triangles in terms of their sides and angles.

  1. HL Congruence Theorem: This theorem is applicable only to right triangles and states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

  2. SAS Congruence Theorem: This theorem states that if two sides of one triangle are equal to two sides of another triangle, and the included angles are equal, then the triangles are congruent.

  3. AAS Congruence Theorem: This theorem states that if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

  4. ASA Congruence Theorem: This theorem states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

If the triangles being compared are right triangles, then the HL (Hypotenuse-Leg) Congruence Theorem would be appropriate. If you have information about equal sides and angles, you could use SAS, AAS, or ASA depending on what is specifically given.

Given the options laid out, if you are specifically dealing with right triangles and have information on their hypotenuse and one leg, you would choose the HL Congruence Theorem.

If you're given something else, you might want to select SAS, AAS, or ASA based on the side-angle relationships presented in the problem.

Without more specific details, for a straightforward scenario, the correct answer is likely HL Congruence Theorem if both triangles contain a right angle. If they do not, then you would need to check for side and angle conditions to apply either SAS, AAS, or ASA as appropriate.