Question

$\overline{vw} \parallel \overline{xy}$. complete the proof that $\triangle vxy \cong \triangle xvw$.

	statement	reason
2	$\overline{vw} \cong \overline{xy}$	given
3	$\angle vxy \cong \angle wvx$
4	$\overline{vx} \cong \overline{vx}$
5	$\triangle vxy \cong \triangle xvw$	sas

Explanation:

Step1: Analyze ∠VXY ≅ ∠WVX

Since \(\overline{VW} \parallel \overline{XY}\), the alternate interior angles theorem applies. When two parallel lines are cut by a transversal (\(\overline{VX}\) here), alternate interior angles are congruent. So \(\angle VXY\) and \(\angle WVX\) are alternate interior angles, hence congruent. Reason: Alternate Interior Angles Theorem.

Step2: Analyze \(\overline{VX} \cong \overline{VX}\)

A segment is congruent to itself by the Reflexive Property of Congruence. So \(\overline{VX}\) is congruent to \(\overline{VX}\) because of the Reflexive Property.

Answer:

For statement 3, the reason is "Alternate Interior Angles Theorem".
For statement 4, the reason is "Reflexive Property of Congruence".