### Video Transcript

Given that π· and πΈ are the
midpoints of line segments π΄π΅ and π΄πΆ, respectively, π΄π· equals 32
centimeters, π΄πΈ equals 19 centimeters, and π·πΈ equals 39 centimeters, find
the perimeter of π·π΅πΆπΈ.

We can begin by filling in the
given length information on the figure of 32 centimeters for π΄π·, 19
centimeters for π΄πΈ, and 39 centimeters for π·πΈ. We can also identify the
information that π· and πΈ are midpoints of their respective line segments. So, πΈπΆ also has a length of
19 centimeters, and π·π΅ has a length of 32 centimeters. We know that we need to work
out the perimeter of this quadrilateral π·π΅πΆπΈ. Weβve worked out three of these
four sides, so we still need to work out the length of the line segment
πΆπ΅. To do this, letβs use the
triangle midsegment theorem.

This theorem states that the
line segment connecting the midpoints of two sides of a triangle is parallel to
the third side and is half its length. This means we can recognize
that line segment πΆπ΅ must be parallel to line segment π·πΈ, and we know
something about the length of line segment πΆπ΅. Since π·πΈ is half the length
of πΆπ΅, we can also write that πΆπ΅ equals two times π·πΈ. We were given that π·πΈ is 39
centimeters, so doubling this, we can calculate that πΆπ΅ is 78 centimeters.

So, we now have enough
information to calculate the perimeter of π·π΅πΆπΈ. Recall that the perimeter is
the distance around the outside edge of a shape. So that means we need to add
the four lengths of 39, 32, 78, and 19 centimeters, which gives us the final
answer that the perimeter of π·π΅πΆπΈ is 168 centimeters.