You are correct in selecting choice A as the answer.
You need the middle angles between the two pairs of given congruent sides, so that you can prove the triangles to be congruent through SAS. The vertical angle theorem is used in this case. Alternate interior angles only come from parallel lines, but we dont know if any of the lines are parallel. Even if we did know the lines were paralle, we still wouldn't use the alternate interior angle theorem.
The part that is necessary in Valerie's proof using SAS to prove ΔVWX ≅ ΔYZX is prove that ∠VWX ≅ ∠YXZ by vertical angles.
The SAS(side angle side) theorem for congruent triangle states that If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
The side WX and XZ are congruent and VX and XZ are congruent . Then the included angles ∠VWX should be congruent to ∠YXZ. The both angles are vertically opposite angles. This can be represented with mathematical symbols below
WX≅XZ
VX ≅XZ
Therefore,
∠VWX ≅ ∠YXZ(vertically opposite angles)
Therefore, the necessary step in Valerie proof is Prove that ∠VWX ≅ ∠YXZ by vertical angles.
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