Question

question 4 of 10
johnny is going to use asa to prove that \\( \triangle vwx \cong \triangle yzx \\).
which of these is a necessary step in johnnys proof?
a. prove that \\( \angle vwx \cong \angle yzx \\) by alternate interior angles.
b. prove that \\( \overline{vw} \cong \overline{yz} \\) by cpctc.
c. prove that \\( \angle vxw \cong \angle yxz \\) by vertical angles.
d. prove that \\( \overline{wx} \cong \overline{xz} \\) by cpctc.

Explanation:

• The ASA (Angle - Side - Angle) congruence criterion requires two angles and the included side to be congruent.
• Vertical angles are congruent. In the given triangles \(\triangle VWX\) and \(\triangle YZX\), \(\angle VXW\) and \(\angle YXZ\) are vertical angles.
• Proving \(\angle VXW\cong\angle YXZ\) (by vertical angles) is a necessary step for using ASA as we already have one pair of angles (\(\angle V\) and \(\angle Y\)) and a pair of sides (marked as congruent) in the given figure.

Answer:

C. Prove that \(\angle VXW\cong\angle YXZ\) by vertical angles.