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