Answer:
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Step-by-step explanation:
To complete the two-column proof, we need to prove that \(\triangle XVZ \cong \triangle WVY\). Here's the completed two-column proof:|
Statements
| Reasons ||-------------------------------------------|--------------------------------|| 1. V is the midpoint of WX and YZ | Given
|| 2. \(\overline{WV} \cong \overline{VX}\) and \(\overline{YV} \cong \overline{VZ}\) | Midpoint definition
|| 3. \(\angle WVY \cong \angle XVZ\) | Vertical angles are congruent || 4. \(\triangle XVZ \cong \triangle WVY\) |
SAS (Side-Angle-Side) Postulate
|Explanation:1. The first statement is given: V is the midpoint of WX and YZ.
2. Since V is the midpoint, it divides WX and YZ into two equal segments. Therefore, \(WV \cong VX\) and \(YV \cong VZ\).
3. The angles \(\angle WVY\) and \(\angle XVZ\) are vertical angles, which are always congruent.
4. With two pairs of congruent sides and the included angle congruent, the triangles are congruent by the SAS Postulate.Please refer to the picture as there are typing errors dear
