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.
