Answer:
To prove that XZ ≅ VW, we can use the given information and the properties of congruent triangles.
Explanation:
1. Given: YW ≅ YZ and XY ≅ VY
2. We want to prove: XZ ≅ VW
To prove the statement, we can use the triangle congruence theorem. If we can show that two triangles are congruent, then their corresponding sides will also be congruent.
3. By the reflexive property, we know that YZ ≅ YZ.
4. Given that YW ≅ YZ and XY ≅ VY, we can conclude that triangle XYW ≅ triangle VYZ by the side-side-side (SSS) congruence criterion.
5. By the corresponding parts of congruent triangles (CPCTC), we can state that angle X ≅ angle V.
6. Now, we can use the congruent triangles XYW and VYZ to establish the congruence of the corresponding sides. By the corresponding sides of congruent triangles (CPCTC), we can conclude that XZ ≅ VW.
Therefore, based on the given information and the congruence of triangles XYW and VYZ, we can prove that XZ ≅ VW.
Keep in mind that this is just one possible approach to proving the statement. Depending on the specific geometric properties and theorems you have learned, there may be alternative methods to prove the congruence of XZ and VW.