Question

y is the midpoint of \\( \overline { wx } \\). complete the proof that \\( \triangle vwy \cong \triangle vxy \\).

	statement	reason
2	\\( \overline { wx } \perp \overline { vy } \\)	given
3	\\( \angle vyw \cong \angle vyx \\)	all right angles are congruent
4	\\( \overline { wy } \cong \overline { xy } \\)	definition of midpoint
5	\\( \overline { vy } \cong \overline { vy } \\)	reflexive property of congruence
6	\\( \triangle vwy \cong \triangle vxy \\)

Explanation:

Step1: Recall the SAS (Side - Angle - Side) 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.

Step2: Identify the sides and included angle for the two triangles \(\triangle VWY\) and \(\triangle VXY\)

• We have \(\overline{WY}\cong\overline{XY}\) (from the definition of mid - point, statement 4).
• \(\angle VYW\cong\angle VYX\) (all right angles are congruent, statement 3).
• \(\overline{VY}\cong\overline{VY}\) (reflexive property of congruence, statement 5).

Answer:

By the SAS (Side - Angle - Side) congruence criterion.