Let's start with examining the given statement, the statement that we want to prove and the figure.
Given: WX ≅ YZ
Prove: WY ≅ XZ
We will write a two-column proof. In our first step, we have stated the given information. Next, we will use the Definition of Congruent Segments to interpret the lengths of the segments.
Definition of Congruent Segments
WX=YZ
Now, we will add XY to both sides of the equation. To do that we will use the Addition Property of Equality.
Addition Property of Equality
WX+ XY= XY+YZ
By the Segment Addition Postulate, we will add the terms on the both sides.
Segment Addition Postulate
WX=XZ
As a final step, we will use the Definition of Congruent Segments to complete the proof.
Definition of Congruent Segments
WY ≅ XZ
Combining these steps, let's form our two-column proof.
