Question Video: Checking if Triangles are Congruent Mathematics • 8th Grade

In the given figure, triangle ๐ด๐ต๐ถ and ๐ต๐ถ๐ท have two equal sides and share one equal angle. Are triangles ๐ด๐ต๐ถ and ๐ต๐ถ๐ท congruent?

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Video Transcript

In the given figure, triangle ๐ด๐ต๐ถ and ๐ต๐ถ๐ท have two equal sides and share one equal angle. Are triangles ๐ด๐ต๐ถ and ๐ต๐ถ๐ท congruent?

Letโ€™s start by highlighting our triangles. We have the slightly larger triangle ๐ด๐ต๐ถ and then we have this slightly smaller triangle marked in orange, ๐ต๐ถ๐ท. As we can clearly see, these are different sizes and therefore would not be congruent. But as we indeed can see, we do have some corresponding sides of equal length. And we do have a corresponding angle of equal length. Perhaps we find some sort of problem with the congruency rules. So letโ€™s note down what we know about each triangle and see if we can work out whatโ€™s happening.

We can see in our diagram that we have two lengths marked as two units, the length ๐ด๐ต and the length ๐ต๐ท, which we could then write as congruent. The line ๐ต๐ถ of length four occurs in both triangles. Finally, we can see that we have a common angle. The angle ๐ด๐ถ๐ต would be equal to the angle ๐ต๐ถ๐ท. It might be tempting then to say that we have a congruency because of a real SSA. But in fact, this is not a congruency rule. Because as we can see from our diagram, we could in fact create two noncongruent triangles using two corresponding pairs of sides congruent and a pair of corresponding angles congruent.

We could have used the congruency rule SAS if the angle was included between the two sides. But itโ€™s not in this diagram. So therefore, we can happily say that our two triangles are not congruent. They didnโ€™t look congruent. And even in the case of a badly drawn diagram, we canโ€™t prove that theyโ€™re congruent.

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