Question

the asa congruence theorem quick check. which of the following pairs of triangles could be proven congruent by the asa congruence theorem? if none

Explanation:

Step1: Identify angles and side

Check for pairs of congruent angles and the included side.

Step2: Apply ASA theorem

If two - angles and included side match, triangles are congruent.

Answer:

We need to check for two - angles and the included side being congruent in each pair of triangles. Without seeing the angle and side markings clearly in the images, assume we have the following analysis for a general case. Let's say we have pairs of triangles and we check for ASA (Angle - Side - Angle) congruence.

1. First, identify the angles and the included side in each pair of triangles.
2. If in a pair, two angles of one triangle are congruent to two angles of the other triangle and the side between those two angles is also congruent, then the triangles are congruent by ASA.

Let's assume for a particular pair (say the first pair in the image), if we have $\angle X\cong\angle A$, $\angle Y\cong\angle B$ and side $XY\cong AB$, then $\triangle XYZ\cong\triangle ABC$ by ASA.

Since we don't have specific markings shown clearly, we can't give a definite answer on which pair is congruent by ASA from the given image. But the general steps to check for ASA congruence are as above.