Are two squares congruent if the side length of one square is equal to the side length of the other?
Here we have two squares. And we know that the side length of one square, call it 𝑥, is equal to the side length of the other, call it 𝑦. So 𝑥 is equal to 𝑦.
So looking at square number one with side length 𝑥, because it’s a square, all side lengths are equal. So we can label them all 𝑥. And we can do the same with the other square. We can label them all 𝑦.
Now another property that we know about a square is that all angles are equal to 90 degrees, which are now labeled. So let’s go ahead and say that length of 𝑥 is five.
So if 𝑥 is five, each of these side lengths will be five. But since 𝑥 is equal to 𝑦, if 𝑥 is five, we can substitute five in for 𝑥 which makes 𝑦 equal to five, which we’ve now labeled.
So are these two squares congruent? If they would be congruent, they will have equal angles and equal side lengths. And we have that! Therefore, our answer is yes.