Q:

Which congruence theorem can be used to prove △WXZ ≅ △YZX? Triangles W X Z and Y Z X share side X Z. Angles W X Z and X Z Y are right angles. Angles X W Z and X Y Z are congruent. AAS ASA SAS HL

Accepted Solution

A:
Answer:The correct option is AAS.Step-by-step explanation:Consider the diagram below.It is provided that The triangles △ WXZ and △ YZX share a side XZ.Angles ∠WXZ and ∠XZY are right angles.Angles ∠XWZ and ∠XYZ are congruent.If two angles are congruent it implies that they are same in degrees or radians.So, the angles ∠XWZ and ∠XYZ are equal.So, in the diagram below, one of the triangles have two angles that are equal to the corresponding angles on the other triangle and the two triangles share a side.Then according to the Angle-Angle-Side (AAS) statement the triangles △ WXZ and △ YZX are congruent.Thus, the correct option is AAS.