Question

Johnny is going to use ASA to prove that VWX=YZX.Which of these is a necessary step in Johnny's proof? A. Prove that WX= XZby CPCTC.B. Prove that VW=YZ by CPCTC.C. Prove that VWX=YZX by alternate interior angles.D. Prove that VXW = YXZ by vertical angles.

Answer 1

In order to prove that two triangles are congruent using the ASA theorem, it is necessary to show two pairs of congruent angles and one pair of congruent sides of the triangles.

In the given diagram, there is already a pair of congruent triangles and a pair of congruent sides shown.

Then, in order to use the ASA theorem, we need to prove that there is another pair of congruent angles, one from each triangle.

Since the side VX must be adjacent to both angles involved in the procedure, then we need to show that the angle VXW is congruent to the angle YXZ, which is adjacent to the side YX.

This can be proven using the fact that VXW and YXZ are vertical angles.

Therefore, the necessary step in Johnny's proof is shown in option D)

$\text{Prove that }\angle VXW\cong\angle YXZ\text{ by vertical angles}$