Question

given: $overline{xw}congoverline{xy}$, $overline{xz}$ bisects $angle wxy$ prove: $\triangle wxzcong\triangle yxz$ statements reasons

Explanation:

Step1: State given side - equality

$\overline{XW}\cong\overline{XY}$ (Given)

Step2: Use angle - bisector property

$\angle WXZ\cong\angle YXZ$ since $\overline{XZ}$ bisects $\angle WXY$ (Definition of angle - bisector)

Step3: Identify common side

$\overline{XZ}\cong\overline{XZ}$ (Reflexive property of congruence)

Step4: Apply SAS congruence criterion

$\triangle WXZ\cong\triangle YXZ$ by the Side - Angle - Side (SAS) congruence postulate

Answer:

Statements	Reasons
$\angle WXZ\cong\angle YXZ$	Definition of angle - bisector
$\overline{XZ}\cong\overline{XZ}$	Reflexive property of congruence
$\triangle WXZ\cong\triangle YXZ$	SAS congruence postulate