Question

What theorem shows that △ACE ≅ △BCD?

Two triangles, A C E and B C D, that meet in the center at C. Congruence marks show that E C is congruent to D C, and A C is congruent to B C.
A. Hypotenuse-Leg
B. Angle-Angle-Side
C. Angle-Side-Angle
D. Side-Angle-Side

Answer 1

The theorem that shows △ACE ≅ △BCD is congruent is the Side-Angle-Side (SAS) Congruence Theorem, as they share two congruent sides and the included angle.

Step-by-step explanation:

The theorem that shows that △ACE ≅ △BCD is the Side-Angle-Side (SAS) Congruence Theorem. This 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, then the triangles are congruent. In the case of △ACE and △BCD, we are given that AC is congruent to BC and EC is congruent to DC, and both triangles share the angle at vertex C, making it the included angle for both triangles. Hence, by the SAS theorem, the triangles are congruent.

Answer 2

The correct theorem that shows that △ACE ≅ △BCD is Side-Angle-Side (SAS) theorem. It 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. In this case, EC and DC are congruent, AC and BC are congruent, and the included angle at C is congruent. Therefore, △ACE ≅ △BCD by SAS.