Video: Using the Properties of Congruence between Two Rectangles

Consider two congruent rectangles 𝐴𝐡𝐢𝐷 and π‘‹π‘Œπ‘πΏ. Which line in π‘‹π‘Œπ‘πΏ corresponds to line segment 𝐴𝐡?

01:33

Video Transcript

Consider two congruent rectangles 𝐴𝐡𝐢𝐷 and π‘‹π‘Œπ‘πΏ. Which line in π‘‹π‘Œπ‘πΏ corresponds to line segment 𝐴𝐡?

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 𝐴𝐡𝐢𝐷 and π‘‹π‘Œπ‘πΏ, 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 𝐴𝐡𝐢𝐷 is congruent to π‘‹π‘Œπ‘πΏ, then that means that each of the vertices have to be in the same corresponding position.

So let’s now consider this line segment 𝐴𝐡. We’re asked which line in π‘‹π‘Œπ‘πΏ 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 𝐴𝐡 will be the line segment π‘‹π‘Œ. We could’ve also discovered this using the congruency relationship. The line segment 𝐴𝐡 corresponds with the line segment π‘‹π‘Œ. Therefore, either by drawing a diagram or by using the congruency statement, we would get the answer of line segment π‘‹π‘Œ.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.