Question

What theorem proves ΔABC≅ΔFED?
Option #1: the SSS Theorem
Option #2: the SAS Theorem
Option #3: the HL Theorem
Option #4: the ASA Theorem

Answer 1

To determine which theorem proves that triangle \( \Delta ABC \) is congruent to triangle \( \Delta FED \), we need to know which sides and angles of the triangles are given. Here's a brief overview of the options:

1. **SSS Congruence Theorem**: States that if three sides of one triangle are equal to three sides of another triangle, the two triangles are congruent.
2. **SAS Congruence Theorem**: States that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
3. **HL Congruence Theorem**: A special case for right triangles, states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.
4. **ASA Congruence 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, the triangles are congruent.

Without more information on the specific sides and angles that are equal, it's not possible to definitively choose the correct theorem.

If you have specific information about the sides and/or angles of triangles \( \Delta ABC \) and \( \Delta FED \), please provide it to identify which theorem applies.