Question

y is the midpoint of \\(\overline{uw}\\) and \\(\overline{vx}\\) and \\(\overline{vw} \cong \overline{ux}\\). prove that \\(\triangle vwy \cong \triangle xuy\\). some of the given information has already been filled in for you.

(image of two triangles with vertices w, v, y and x, u, y, intersecting at y. below is a table with statement and reason columns. rows 1: y is the midpoint of \\(\overline{uw}\\), reason: given. row 2: y is the midpoint of \\(\overline{vx}\\), reason: given. row 3: empty for statement and reason.)

Explanation:

Step1: Derive segment congruence from midpoint

From midpoint definition: $\overline{VY} = \overline{XY}$, so $\overline{VY} \cong \overline{XY}$

Step2: Derive second segment congruence

From midpoint definition: $\overline{WY} = \overline{UY}$, so $\overline{WY} \cong \overline{UY}$

Step3: State given triangle side congruence

$\overline{VW} \cong \overline{UX}$ (Given)

Step4: Apply SSS congruence

Three pairs of sides are congruent, so $\triangle VWY \cong \triangle XUY$ by SSS Postulate

Answer:

Statement	Reason
2. $Y$ is the midpoint of $\overline{VX}$	Given
3. $\overline{VY} \cong \overline{XY}$	Definition of midpoint
4. $\overline{WY} \cong \overline{UY}$	Definition of midpoint
5. $\overline{VW} \cong \overline{UX}$	Given
6. $\triangle VWY \cong \triangle XUY$	SSS Congruence Postulate