Question

fill in the blank 1 point
complete the proof.
copy the diagram to your show your work page to mark congruent segments or angles.
given: \\( \overline{ty} \cong \overline{yx}, \angle tvy \cong \angle xwy \\)
prove: \\( \triangle tvy \cong \triangle xwy \\)

Explanation:

Step1: Identify the Side - Angle - Side (SAS) 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. In this case, we have \(\overline{TY}\cong\overline{YX}\) (given as statement 1), \(\angle VYT\cong\angle WYX\) (statement 2, which is the included angle), and \(\overline{VY}\cong\overline{WY}\) (common side).

Step2: Apply the SAS congruence criterion

Since we have two sides (\(\overline{TY}\cong\overline{YX}\) and \(\overline{VY}\cong\overline{WY}\)) and the included angle (\(\angle VYT\cong\angle WYX\)) congruent, by the Side - Angle - Side (SAS) congruence criterion, \(\triangle TVY\cong\triangle XWY\).

Answer:

1. \(VY = WY\) (Common side, reflexive property of congruence). 3. \(SAS\) (Side - Angle - Side congruence criterion)