Answer: SAS congruence (choice C)
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Explanation:
Let's go through the various answer choices. I'll say whether or not they are used
A) This is used because angle WXZ = angle WYZ and angle WZX = angle ZWY are the two pairs of angles. The pair of sides are WZ = WZ which overlap (aka shared) between the two triangles. Note how the sides are not between the angled mentioned. Eg: for the triangle on the left, WZ is not between angle WXZ and angle WZX. So we can cross choice A off the list. Note: AAS is slightly different from ASA. Make sure not to confuse the two.
B) We use this to prove that the right angles (WXZ and WYZ) are congruent to each other. Both are 90 degrees. This will then feed in to choice A above, to help use AAS. We can cross choice B off the list.
C) We do not use SAS because we use AAS instead. We only have info about one pair of sides (WZ = WZ). We do not have info about another pair of sides. Therefore, this is the answer.
D) We use this fact to help set up that angle WZX = angle ZWY. The segments WY and XZ are parallel. I like to think of them as train tracks. On the inside of the train tracks are the angles WZX and ZWY, and they are on opposite sides of the transversal segment WZ, so this is why the pair of angles are alternate interior angles. They are congruent as long as WY is parallel to XZ. Like with choice B, this helps feed into choice A. We can cross choice D off the list.
