Question

1. complete the proof.

given: ( wx = xy ), ( vx = xz )
prove: ( angle wvx cong angle yzx )

statements	reasons
2.	2. vertical angles theorem
3. ( \triangle vxw cong \triangle yxz )	3.
4.	4.

Explanation:

Step1: State the given

Given \( WX = XY\) and \(VX = XZ\) (Reason: Given)

Step2: Identify vertical angles

\(\angle VXW=\angle YXZ\) (Reason: Vertical Angles Theorem)

Step3: Prove triangle congruence

\(\triangle VXW\cong\triangle YXZ\) (Reason: Side - Angle - Side (SAS) congruence criterion, since \(VX = XZ\), \(\angle VXW=\angle YXZ\), \(WX = XY\))

Step4: Conclude angle congruence

\(\angle WVX\cong\angle YZX\) (Reason: Corresponding parts of congruent triangles are congruent (CPCTC))

Answer:

Statements	Reasons
2. \(\angle VXW=\angle YXZ\)	2. Vertical Angles Theorem
3. \(\triangle VXW\cong\triangle YXZ\)	3. SAS (Side - Angle - Side)
4. \(\angle WVX\cong\angle YZX\)	4. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)