### Video Transcript

In the figure shown, πΈ, πΉ,
and π· are the midpoints of line segments π΅πΆ, π΄π΅, and π΄πΆ,
respectively. Find the perimeter of triangle
πΈπΉπ·.

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. πΈ, πΉ, and π· bisect their
respective line segments. So, in order to find the
perimeter of triangle πΈπΉπ·, thatβs the distance around the outside edge, weβll
need to calculate the lengths of the three line segments πΉπ·, π·πΈ, and
πΈπΉ.

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. Letβs look at line segment
πΉπ·. Line segment πΉπ· 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 π΅πΆ. The length of π΅πΆ is given as
4.6 centimeters, so half of this is 2.3 centimeters.

Now, letβs see if we can do the
same to calculate the lengths of the other two sides in triangle πΈπΉπ·. We can consider the line
segment π·πΈ next. Line segment π·πΈ joins the
midpoints of two sides of a triangle, because it joins π·, the midpoint of line
segment π΄πΆ, and πΈ, the midpoint of line segment π΅πΆ. Therefore, we know that it must
be half the length of line segment π΄π΅, 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 πΈπΉ. It joins midpoints πΈ and
πΉ. So, the length of πΈπΉ will be
half of line segment π΄πΆ; half of 6.2 centimeters is 3.1 centimeters.

And now to find the perimeter
of triangle πΈπΉπ·, 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 πΈπΉπ· is 8.15 centimeters.