Question Video: Using the Properties of Congruence between Two Rectangles

Video Transcript

Consider two congruent rectangles 𝐴𝐵𝐶𝐷 and 𝑋𝑌𝑍𝐿. Which line in 𝑋𝑌𝑍𝐿 corresponds to line segment 𝐴𝐵?

Let’s begin by noting that we have two rectangles which are described as congruent, which means the same shape and size. This means that in our rectangles 𝐴𝐵𝐶𝐷 and 𝑋𝑌𝑍𝐿, corresponding pairs of angles will be congruent and corresponding pairs of sides will be congruent. Let’s try modeling the two rectangles. So, we could draw them like this or even like this. What we do have to be careful of, however, is that because we have this congruency relationship that 𝐴𝐵𝐶𝐷 is congruent to 𝑋𝑌𝑍𝐿, then that means that each of the vertices have to be in the same corresponding position.

So let’s now consider this line segment 𝐴𝐵. We’re asked which line in 𝑋𝑌𝑍𝐿 corresponds to this one. Using either of the options that we used to draw our two rectangles, the line segment that will be in the same corresponding position to line segment 𝐴𝐵 will be the line segment 𝑋𝑌. We could’ve also discovered this using the congruency relationship. The line segment 𝐴𝐵 corresponds with the line segment 𝑋𝑌. Therefore, either by drawing a diagram or by using the congruency statement, we would get the answer of line segment 𝑋𝑌.