Question

given: v is the midpoint of $overline{wz}$ and $overline{xy}$
prove: $\triangle wxvcong\triangle zyv$
statements

1. v is the midpoint of $overline{wz}$ and $overline{xy}$
2. $overline{wv}congoverline{zv}$
3. $angle wvxcongangle zvy$
4. $overline{xv}congoverline{yv}$
5. $\triangle wxvcong\triangle zyv$

reasons
1.
2.
3.
4.
5.

Explanation:

Step1: Given information

Given

Step2: Mid - point property

A mid - point divides a line segment into two congruent segments

Step3: Vertical angles are congruent

Vertical angles are equal

Step4: Mid - point property

A mid - point divides a line segment into two congruent segments

Step5: SAS (Side - Angle - Side) congruence criterion

Two sides and the included angle are congruent

Answer:

1. Given
2. Definition of mid - point
3. Vertical angles are congruent
4. Definition of mid - point
5. SAS congruence criterion