Explanation:

Let’s break it down:

- We know m?C = m?Z and AC = XZ. That means, in ?ABC and ?XYZ, we already have an angle and its adjacent side equal.

- For triangles to be congruent, you need one of the congruence criteria: ASA, SAS, SSS, or AAS.

Let’s look at the options:

- Option 1: AB = AC

This just tells you two sides in one triangle are equal. It doesn't connect triangle ABC to triangle XYZ. No congruence between the two triangles yet.

- Option 2: BC = YZ

Now, you have AC = XZ, BC = YZ, and included angle C = Z. That’s the SAS (side-angle-side) criterion directly between the two triangles.

- Option 3: AB = XY

If AB = XY and still only one angle (C=Z) is common, not enough info for congruence—angles aren’t included between the known sides.

- Option 4: BC = AB

This only tells you two sides of triangle ABC are equal. It says nothing about triangle XYZ, so it doesn’t help for congruence.

So, what this really means is:

Option 2 (BC = YZ) is necessary.

You get two sides and the included angle equal—classic SAS. Radiantly clear.