Question

△vwz and △xyz are equilateral. complete the proof that △vyz ≅ △wxz.

1\tstatement: △vwz is equilateral\treason: given
2\tstatement: △xyz is equilateral\treason: given
3\tstatement: (overline{vz} cong overline{wz})\treason: definition of equilateral triangle
4\tstatement: (overline{xz} cong overline{yz})\treason: definition of equilateral triangle
5\tstatement: (angle vzy cong angle wzx)\treason: vertical angle theorem
6\tstatement: △vyz ≅ △wxz\treason: options: aas, asa, cpctc, definition of congruence, sas, sss

Explanation:

Step1: Identify side pairs

We have $\overline{VZ} \cong \overline{WZ}$ (from equilateral $\triangle VWZ$), $\overline{XZ} \cong \overline{YZ}$ (from equilateral $\triangle XYZ$).

Step2: Identify included angle

$\angle VZY \cong \angle WZX$ (vertical angles are congruent).

Step3: Match congruence rule

We have two pairs of congruent sides and the included congruent angle, which fits the SAS (Side-Angle-Side) congruence criterion.

Answer:

SAS