Question

determine whether the triangles must be congruent. if so, name the postulate or theorem that best justifies your answer. if not, explain.
choose the correct answer below.
a. the triangles are congruent by sss.
b. the triangles are congruent by asa.
c. the triangles are congruent by sas.
d. the triangles are congruent by aas.
e. the triangles are not congruent.

Explanation:

• Identify the common side: In the given figure, \(ZX = ZX\) (common side).
• Check the angles: The two angles at \(X\) are equal (marked as equal in the figure).
• Check the sides: Assume \(WX = XY\) (if we consider the two - triangle division from the given figure structure).
• Apply the SAS (Side - Angle - Side) congruence criterion: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent. Here, if \(WX = XY\), \(\angle WXZ=\angle YXZ\), and \(ZX = ZX\), the SAS criterion is satisfied.

Answer:

C. The triangles are congruent by SAS.