# Question Video: Finding the Perimeter of a Quadrilateral Using the Triangle Midsegment Theorem Mathematics

Given that π· and πΈ are the midpoints of line segments π΄π΅ and π΄πΆ respectively, π΄π· = 32 cm, π΄πΈ = 19 cm, and π·πΈ = 39 cm, find the perimeter of π·π΅πΆπΈ.

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### Video Transcript

Given that π· and πΈ are the midpoints of line segments π΄π΅ and π΄πΆ, respectively, π΄π· equals 32 centimeters, π΄πΈ equals 19 centimeters, and π·πΈ equals 39 centimeters, find the perimeter of π·π΅πΆπΈ.

We can begin by filling in the given length information on the figure of 32 centimeters for π΄π·, 19 centimeters for π΄πΈ, and 39 centimeters for π·πΈ. We can also identify the information that π· and πΈ are midpoints of their respective line segments. So, πΈπΆ 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΅πΆπΈ. Weβve worked out three of these four sides, so we still need to work out the length of the line segment πΆπ΅. To do this, letβs 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 πΆπ΅ must be parallel to line segment π·πΈ, and we know something about the length of line segment πΆπ΅. Since π·πΈ is half the length of πΆπ΅, we can also write that πΆπ΅ equals two times π·πΈ. We were given that π·πΈ is 39 centimeters, so doubling this, we can calculate that πΆπ΅ is 78 centimeters.

So, we now have enough information to calculate the perimeter of π·π΅πΆπΈ. 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΅πΆπΈ is 168 centimeters.