Question

given: $overline{yz}$ bisects $angle wyx$, $angle ywzcongangle yxz$. prove: $\triangle wyzcong\triangle xyz$. statement 1. $overline{yz}$ bisects $angle wyx$ 2. $angle ywzcongangle yxz$ 3. $overline{yz}congoverline{zy}$ 4. $angle wyzcongangle xyz$ 5. $\triangle wyzcong\triangle xyz$. reason 1. 2. 3. 4. 5. given sss sas aas asa hl definition of midpoint definition of angle bisector reflexive property corresponding angles alternate interior angles vertical angles

Explanation:

Step1: Given information

1. $\overline{YZ}$ bisects $\angle WYX$ - Given
2. $\angle YWZ\cong\angle YXZ$ - Given

Step2: Reflexive property

$\overline{YZ}\cong\overline{ZY}$ because any segment is congruent to itself (Reflexive Property)

Step3: Angle - bisector definition

Since $\overline{YZ}$ bisects $\angle WYX$, by the Definition of Angle Bisector, $\angle WYZ\cong\angle XYZ$

Step4: Prove congruence

In $\triangle WYZ$ and $\triangle XYZ$, we have $\angle YWZ\cong\angle YXZ$, $\angle WYZ\cong\angle XYZ$ and $\overline{YZ}\cong\overline{ZY}$. So, by the Angle - Angle - Side (AAS) congruence criterion, $\triangle WYZ\cong\triangle XYZ$

Answer:

1. Given
2. Given
3. Reflexive Property
4. Definition of Angle Bisector
5. AAS