Question

what theorem is used to show (\triangle abccong\triangle xyz)? add text

Explanation:

Step1: Recall triangle congruence theorems

Triangle congruence theorems include SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - angled triangles).

Step2: Analyze the given triangles

In the two triangles, we can see that two sides and the included angle are marked as equal.

Step3: Identify the theorem

The Side - Angle - Side (SAS) 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 two triangles are congruent.

Answer:

The SAS (Side - Angle - Side) theorem is used to show that $\triangle ABC\cong\triangle XYZ$.