Question

in the diagram below, $angle yzxcongangle wvx$ and $\triangle zxv$ is an equilateral triangle. also, $overline{zw}$ and $overline{vy}$ intersect at point $x$.
complete the proof that $\triangle zyxcong\triangle vwx$.

Explanation:

Step1: Vertical angles theorem

Vertical angles are congruent. Since \(\angle ZXY\) and \(\angle VXW\) are vertical angles, \(\angle ZXY\cong\angle VXW\)

Step2: ASA (Angle - Side - Angle) congruence criterion

We have \(\angle YZX\cong\angle WVX\) (given), \(\overline{ZX}\cong\overline{VX}\) (from the definition of an equilateral triangle), and \(\angle ZXY\cong\angle VXW\) (vertical angles). By the ASA congruence criterion, \(\triangle ZYX\cong\triangle VWX\)

Answer:

1. Vertical angles theorem; 5. ASA (Angle - Side - Angle) congruence criterion