Question

wx ≅ yz, ∠txz ≅ ∠vyw, and ∠t ≅ ∠v. complete the proof that △vwy ≅ △tzx.

1 wx ≅ yz given
2 ∠txz ≅ ∠vyw given
3 ∠t ≅ ∠v given
4 xz = yz + xy additive property of length
5 wy = wx + xy additive property of length
6 xz = wx + xy substitution
7 wy = xz transitive property of equality
8
9

Explanation:

Step1: Identify the triangles and given congruencies

We have \(\triangle VTWY\) and \(\triangle TZX\). We know \(\angle T\cong\angle V\), \(\angle TXZ\cong\angle VYW\) (from step 2), and \(WY = XZ\) (from step 7).

Step2: Apply the AAS (Angle - Angle - Side) congruence criterion

The AAS congruence criterion states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
In \(\triangle VWY\) and \(\triangle TZX\):

• \(\angle T\cong\angle V\) (given)
• \(\angle TXZ\cong\angle VYW\) (given)
• \(WY = XZ\) (from step 7, which is a non - included side for the given angles)

Answer:

Statement	Reason