Question

To determine what else needs to be congruent to show that triangle ABC is congruent to triangle XYZ by the ASA (Angle-Side-Angle) congruence postulate, you can use the given information and the properties of ASA congruence. Here is a multiple-choice question:

What else would need to be congruent to show that ΔABC ≅ ΔXYZ by ASA?

A. ZB = ZY
B. AC = XZ
C. BC = YZ
D. ∠C = ∠Z

Answer 1

To show that triangle ABC is congruent to triangle XYZ using the ASA postulate, we need to identify a corresponding side between two congruent angles. Option B, AC = XZ, is the correct choice as it represents the side between two angles that need to be congruent as per the ASA criteria.

Step-by-step explanation:

To prove that triangle ABC is congruent to triangle XYZ by the ASA congruence postulate, we must identify two angles and the side between them that are congruent in both triangles. If we are given one angle and one side that are congruent, we need one more angle to satisfy ASA criteria. From the choices provided:

• A: ZB = ZY does not align with either angle or side between the angles in the triangles.
• B: AC = XZ is correct as it represents the side between the two congruent angles.
• C: BC = YZ is a side, but we need an angle for ASA.
• D: ∠C = ∠Z is an angle, but not the one between the two congruent sides we are considering for ASA.

Therefore, option B is needed in conjunction with the other given congruent parts to use the ASA postulate.