Video Transcript
In the figure shown, 𝐸, 𝐹,
and 𝐷 are the midpoints of line segments 𝐵𝐶, 𝐴𝐵, and 𝐴𝐶,
respectively. Find the perimeter of triangle
𝐸𝐹𝐷.
We should note that from the
information we are given and the markings on the diagram, that we have three
midpoints of line segments here. 𝐸, 𝐹, and 𝐷 bisect their
respective line segments. So, in order to find the
perimeter of triangle 𝐸𝐹𝐷, that’s the distance around the outside edge, we’ll
need to calculate the lengths of the three line segments 𝐹𝐷, 𝐷𝐸, and
𝐸𝐹.
Now, because we know that there
are some midpoints of lines, that might make us wonder if we could possibly
apply one of the triangle midsegment theorems. We can recall that the length
of the line segment joining the midpoints of two sides of a triangle is equal to
half the length of the third side. Let’s look at line segment
𝐹𝐷. Line segment 𝐹𝐷 is a line
segment joining the midpoints of two sides of a triangle. Therefore, its length is going
to be half the length of the third side, which is line segment 𝐵𝐶. The length of 𝐵𝐶 is given as
4.6 centimeters, so half of this is 2.3 centimeters.
Now, let’s see if we can do the
same to calculate the lengths of the other two sides in triangle 𝐸𝐹𝐷. We can consider the line
segment 𝐷𝐸 next. Line segment 𝐷𝐸 joins the
midpoints of two sides of a triangle, because it joins 𝐷, the midpoint of line
segment 𝐴𝐶, and 𝐸, the midpoint of line segment 𝐵𝐶. Therefore, we know that it must
be half the length of line segment 𝐴𝐵, which is the third side of the
triangle. Half of 5.5 centimeters is 2.75
centimeters. And we can do the same for the
length of line segment 𝐸𝐹. It joins midpoints 𝐸 and
𝐹. So, the length of 𝐸𝐹 will be
half of line segment 𝐴𝐶; half of 6.2 centimeters is 3.1 centimeters.
And now to find the perimeter
of triangle 𝐸𝐹𝐷, we add these three calculated lengths together. 2.3 plus 2.75 plus 3.1 is equal
to 8.15 centimeters. And so, by applying the
triangle midsegment theorem three times, we have determined that the perimeter
of triangle 𝐸𝐹𝐷 is 8.15 centimeters.
