Question

△uvx is equilateral, ∠wvx ≅ ∠xuy, and (overline{vw}congoverline{uy}). complete the proof that △vwx ≅ △uyx.

statement
1 △uvx is equilateral
2 ∠wvx ≅ ∠xuy
3 (overline{vw}congoverline{uy})
4 (overline{ux}congoverline{vx})
5

reason
given
given
given
definition of equilateral triangle

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Identify the sides and angle for \(\triangle VWX\) and \(\triangle UYX\)

We are given that \(\overline{VW}\cong\overline{UY}\) (side), \(\angle VWX\cong\angle XUY\) (angle), and \(\overline{UX}\cong\overline{VX}\) (side from the definition of an equilateral triangle \(\triangle UVX\)).

Answer:

\(\triangle VWX\cong\triangle UYX\) by the SAS (Side - Angle - Side) congruence criterion.