Question

Given: WY = XZ

Prove: WX = YZ
Which property or theorem is used to prove this statement?
a) Substitution property
b) Subtraction property
c) Definition of congruence
d) Transitive property

Answer 1

The transitive property of equality is used to prove that WX = YZ given that WY = XZ by demonstrating that if both segments are equal to a third segment, they are equal to each other.

Step-by-step explanation:

To prove that WX = YZ given that WY = XZ, we can use the transitive property of equality. The transitive property states that if two things are equal to the same thing, they are equal to each other. In this case, we assume that WY and XZ are both equal to some segment length a. This means WX (which is WY minus segment YX) and YZ (which is XZ minus segment YX) both equal a minus the length of YX, and therefore, WX = YZ.