Question

given: $overline{vz}congoverline{wx}$, $overline{vy}congoverline{wy}$, y is the mid - point of $overline{zx}$. prove: $\triangle vyzcong\triangle wyx$. complete the statements in the two - column proof. statements: 1. $overline{vz}congoverline{wx}$, $overline{vy}congoverline{wy}$ 2. y is the mid - point of $overline{zx}$ 3. side $squarecong$ side $square$ 4. $\triangle vyzcong\triangle wyx$. reasons: 1. given 2. given 3. definition of mid - point 4. sss. enter your answers in the boxes.

Explanation:

Step1: Identify given congruent sides

$\overline{VZ} \cong \overline{WX}$; $\overline{VY} \cong \overline{WY}$ (Given)

Step2: Use midpoint definition

Y is midpoint of $\overline{ZX}$ (Given) $\implies \overline{ZY} \cong \overline{YX}$ (Definition of midpoint)

Step3: Apply SSS congruence

$\overline{VZ} \cong \overline{WX}$, $\overline{VY} \cong \overline{WY}$, $\overline{ZY} \cong \overline{YX} \implies \triangle VYZ \cong \triangle WYX$ (SSS)

Answer:

1. side ZY ≅ side YX