Question

Given: (WY = XZ)

Prove: (WX = YZ)

a) Substitution property
b) Subtraction property
c) Definition of congruence
d) Transitive property

Answer 1

To prove WX = YZ given WY = XZ, the Subtraction Property is applied to demonstrate that XY = YZ. Then, the Transitive Property proves WX = YZ, provided that we regard XY and YZ as segments of straight line XYZ.

Step-by-step explanation:

The subject of this question is Mathematics. To prove that WX = YZ given that WY = XZ, we can use the Subtraction Property of equality.

1. WY = XZ (Given)
2. WY - WY = XZ - WY (Subtract WY from both sides)
3. 0 = XZ - WY (Anything minus itself is 0)
4. Since WY = XZ, this can be rewritten as 0 = WX + XY - (WX + YZ) (By segment addition)
5. 0 = WX + XY - WX - YZ (Distribute the subtraction)
6. 0 = XY - YZ (The terms WX cancel out)
7. XY = YZ (If the difference is 0, the segments are equal)
8. Therefore, WX = YZ by the Transitive Property of equality. Because if XY = YZ and XYZ is a straight line, then WX = XY + YZ