# Question Video: Applying the Triangle Midsegment Theorem to Solve a Problem Mathematics

In the figure shown, πΈ, πΉ, and π· are the midpoints of line segments π΅πΆ, π΄π΅, and π΄πΆ, respectively. Find the perimeter of β³πΈπΉπ·.

03:11

### Video Transcript

In the figure shown, πΈ, πΉ, and π· are the midpoints of line segments π΅πΆ, π΄π΅, and π΄πΆ, respectively. Find the perimeter of triangle πΈπΉπ·.

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. πΈ, πΉ, and π· bisect their respective line segments. So, in order to find the perimeter of triangle πΈπΉπ·, thatβs the distance around the outside edge, weβll need to calculate the lengths of the three line segments πΉπ·, π·πΈ, and πΈπΉ.

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. Letβs look at line segment πΉπ·. Line segment πΉπ· 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΅πΆ. The length of π΅πΆ is given as 4.6 centimeters, so half of this is 2.3 centimeters.

Now, letβs see if we can do the same to calculate the lengths of the other two sides in triangle πΈπΉπ·. We can consider the line segment π·πΈ next. Line segment π·πΈ joins the midpoints of two sides of a triangle, because it joins π·, the midpoint of line segment π΄πΆ, and πΈ, the midpoint of line segment π΅πΆ. 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 πΈπΉ. It joins midpoints πΈ and πΉ. So, the length of πΈπΉ will be half of line segment π΄πΆ; half of 6.2 centimeters is 3.1 centimeters.

And now to find the perimeter of triangle πΈπΉπ·, 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 πΈπΉπ· is 8.15 centimeters.