dyani wrote a proof to show that $ \angle xwy \cong \angle yzx $. what is her error?
since $ \angle wxz \cong \angle zyw $,
$ \angle xzw \cong \angle ywz $, and $ \overline{xw} \cong \overline{yz} $, by
aas, $ \triangle xwz \cong \triangle yzw $. therefore,
by cpctc, $ \angle xwy \cong \angle yzx $.

choose the correct answer below.
a. $ \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.
b. $ \angle xwy $ and $ \angle yzx $ are congruent because they are angles in an isosceles triangle. so cpctc cannot be used to show the angies congruent.
c. $ \triangle xwz $ and $ \triangle yzw $ are not congruent by aas. they are congruent by asa.
d. $ \angle xwy $ and $ \angle yzx $ are not in $ \triangle xwz $ and $ \triangle yzw $, so cpctc cannot be used for them

Question

dyani wrote a proof to show that $ \angle xwy \cong \angle yzx $. what is her error?
since $ \angle wxz \cong \angle zyw $,
$ \angle xzw \cong \angle ywz $, and $ \overline{xw} \cong \overline{yz} $, by
aas, $ \triangle xwz \cong \triangle yzw $. therefore,
by cpctc, $ \angle xwy \cong \angle yzx $.

choose the correct answer below.
a. $ \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.
b. $ \angle xwy $ and $ \angle yzx $ are congruent because they are angles in an isosceles triangle. so cpctc cannot be used to show the angies congruent.
c. $ \triangle xwz $ and $ \triangle yzw $ are not congruent by aas. they are congruent by asa.
d. $ \angle xwy $ and $ \angle yzx $ are not in $ \triangle xwz $ and $ \triangle yzw $, so cpctc cannot be used for them

Accepted Answer

# Brief Explanations:
CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can only be used for parts (angles or sides) of the congruent triangles. $\angle XWY$ and $\angle YZX$ are not angles of $\triangle XWZ$ and $\triangle YZW$. So, using CPCTC on them is incorrect.

# Answer:
D. $\angle XWY$ and $\angle YZX$ are not in $\triangle XWZ$ and $\triangle YZW$, so CPCTC cannot be used for them

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