Question

\overline { vx } \cong \overline { uw }, \angle uvx \cong \angle vuw, and \overline { wx } \parallel \overline { uv }. complete the proof that \triangle vwx \cong \triangle u x w.

Explanation:

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

Two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle.

Step2: Identify the congruent parts for \(\triangle VWX\) and \(\triangle U X W\)

We know that \(\overline{VX}\cong\overline{UW}\) (given), \(\angle VXW\cong\angle U W X\) (from step 7), and \(\overline{WX}\cong\overline{WX}\) (reflexive property of congruence).

Step3: Apply the ASA congruence criterion

For \(\triangle VWX\) and \(\triangle U X W\), we have:

• \(\angle VXW\) and \(\angle U W X\) (angles)
• \(\overline{VX}\) and \(\overline{UW}\) (sides)
• \(\overline{WX}\) (common side, which is the included side between the angles)

Answer:

\(\triangle VWX\cong\triangle U X W\) (by ASA congruence criterion)