Question

aas proof #2 given: ∠xwz ≅ ∠xyz, xz bisects ∠wxy prove: △xwz ≅ △xyz statements reasons

Explanation:

Step1: State given angle equality

$\angle XWZ\cong\angle XYZ$ (Given)

Step2: Use angle - bisector property

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

Step3: Identify common side

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

Step4: Apply AAS congruence criterion

$\triangle XWZ\cong\triangle XYZ$ (AAS congruence: two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle)

Answer:

Statements	Reasons
$\overline{XZ}$ bisects $\angle WXY$	Given
$\angle WXZ\cong\angle YXZ$	Definition of angle - bisector
$\overline{XZ}\cong\overline{XZ}$	Reflexive property of congruence
$\triangle XWZ\cong\triangle XYZ$	AAS congruence