Question

Given X is the midpoint of WY, WX ≅ XZ Prove XY ≅ XZ

1. X is the midpoint of WY
2. WX = XY
3. WX ≅ XZ
4. WX = XZ
5. XY = XZ
6. XY ≅ XZ

Answer 1

To prove segments XY and XZ are congruent, we apply the transitive property using the given that X is the midpoint of WY and WX is congruent to XZ, leading to the conclusion that XY is congruent to XZ.

Step-by-step explanation:

The question involves proving that segments XY and XZ are congruent using a set of given information. To start the proof, acknowledgment is made that X is the midpoint of WY, which gives us that WX = XY. Next, it is given that WX is congruent to XZ, and due to the congruence, we can state WX = XZ. Since WX equals both XY and XZ in length, we can infer that XY also equals XZ in length, which leads to the conclusion that XY is congruent to XZ. This logical progression follows the transitive property of equality which is fundamental in geometry proofs.