Video: Finding the Perimeter of a Triangle Using the Congruence of Triangles

Triangles ๐ด๐ต๐ถ and ๐ธ๐ท๐น are congruent. What is the perimeter of โ–ณ๐ด๐ต๐ถ?

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Video Transcript

Triangles ๐ด๐ต๐ถ and ๐ธ๐ท๐น are congruent. What is the perimeter of triangle ๐ด๐ต๐ถ?

So here we have two triangles which weโ€™re told are congruent. That means theyโ€™re the same shape and size. More specifically, we can say that corresponding sides are equal and corresponding pairs of angles are equal. We might therefore look at our triangles and note that we have a side of 10 centimeters, a side of 11 centimeters, and, on triangle ๐ด๐ต๐ถ, we have a side of eight centimeters. We might guess that side ๐ธ๐ท is eight centimeters, but letโ€™s check.

We can use the congruency relationship and the order of letters to help us here. If we look at side ๐ท๐น on triangle ๐ธ๐ท๐น, thatโ€™s going to be congruent with side ๐ต๐ถ on triangle ๐ด๐ต๐ถ. So that means theyโ€™ll both be 11 centimeters long. Next, if we look at side ๐ธ๐น on triangle ๐ธ๐ท๐น, thatโ€™s going to correspond with the length ๐ด๐ถ on triangle ๐ด๐ต๐ถ. And that means that ๐ด๐ถ is also 10 centimeters long.

The two final sides on each triangle, thatโ€™s side ๐ด๐ต on triangle ๐ด๐ต๐ถ and side ๐ธ๐ท on triangle ๐ธ๐ท๐น, will also be the same length of eight centimeters. Weโ€™re asked to find the perimeter of triangle ๐ด๐ต๐ถ. Thatโ€™s the distance around the outside. So we take our three lengths of 10, 11, and eight centimeters and add them together, which gives us a perimeter of 29 centimeters.

Note that we have the length unit of centimeters rather than square centimeters, which would be an area. Note that if we choose triangle ๐ธ๐ท๐น instead, we wouldโ€™ve found the same value for the perimeter as two congruent triangles would have the same perimeter.

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