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

Triangles 𝐴𝐵𝐶 and 𝐸𝐷𝐹 are congruent. What is the perimeter of △𝐴𝐵𝐶?

01:55

### Video Transcript

Triangles 𝐴𝐵𝐶 and 𝐸𝐷𝐹 are congruent. What is the perimeter of triangle 𝐴𝐵𝐶?

So here we have two triangles which we’re told are congruent. That means they’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 𝐴𝐵𝐶, we have a side of eight centimeters. We might guess that side 𝐸𝐷 is eight centimeters, but let’s check.

We can use the congruency relationship and the order of letters to help us here. If we look at side 𝐷𝐹 on triangle 𝐸𝐷𝐹, that’s going to be congruent with side 𝐵𝐶 on triangle 𝐴𝐵𝐶. So that means they’ll both be 11 centimeters long. Next, if we look at side 𝐸𝐹 on triangle 𝐸𝐷𝐹, that’s going to correspond with the length 𝐴𝐶 on triangle 𝐴𝐵𝐶. And that means that 𝐴𝐶 is also 10 centimeters long.

The two final sides on each triangle, that’s side 𝐴𝐵 on triangle 𝐴𝐵𝐶 and side 𝐸𝐷 on triangle 𝐸𝐷𝐹, will also be the same length of eight centimeters. We’re asked to find the perimeter of triangle 𝐴𝐵𝐶. That’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 𝐸𝐷𝐹 instead, we would’ve found the same value for the perimeter as two congruent triangles would have the same perimeter.