Question

Given: angle 1 = angle 4; angle 2 = angle 3. Prove: ab = cd. Which of the following triangle congruence theorems would be used in this proof?

1) SSS
2) SAS
3) ASA

Answer 1

To prove AB = CD with the given angles, the Angle-Side-Angle (ASA) congruence theorem is most likely applicable, assuming there is a side between the given angles that belongs to both triangles.

Step-by-step explanation:

To prove that AB = CD using the information that angle 1 = angle 4 and angle 2 = angle 3, we need to establish the congruence of two triangles that these angles and sides are part of. The congruence postulates that could be applicable here are Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Side-Angle (ASA). Given that we know two pairs of angles are equal, we would need a side in common, or information about the sides adjacent to the angles, to use SAS or ASA. Without additional information on the sides, we cannot directly apply SSS.

Therefore, with the given information, the most likely congruence theorem to be used is ASA, as we have two angles and the side between them (if this side is known or can be proven to be common to both triangles). Once we establish triangle congruence using ASA, we can conclude that AB = CD based on corresponding parts of congruent triangles being equal (CPCTC).