Question

dyani wrote a proof to show that ∠xwy≅∠yzx. what is her error? since ∠wxz≅∠zyw, ∠xzw≅∠ywz, and xw≅yz, by aas, △xwz≅△yzw. therefore, by cpctc, ∠xwy≅∠yzx. x choose the correct answer below. a. △xwz and △yzw are not congruent by aas. they are congruent by asa. b. △xwz and △yzw cannot be shown to be congruent with the given information, so cpctc cannot be used to show the angles congruent. c. ∠xwy and ∠yzx are congruent because they are angles in an isosceles triangle, not because of cpctc.

Explanation:

Step1: Analyze congruence postulates

The given proof claims $\triangle XWZ\cong\triangle YZW$ by AAS. But the information provided does not satisfy AAS. AAS requires two - angles and a non - included side to be congruent. Here, the congruence of the triangles cannot be established with the given information.

Step2: Understand CPCTC

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can only be used when the triangles are proven congruent. Since $\triangle XWZ$ and $\triangle YZW$ cannot be shown to be congruent with the given information, CPCTC cannot be used to show $\angle XWY\cong\angle YZX$.

Answer:

B. $\triangle XWZ$ and $\triangle YZW$ cannot be shown to be congruent with the given information, so CPCTC cannot be used to show the angles congruent.