# Question Video: Finding the Unknown Lengths in a Triangle given the Other Sidesโ Lengths Using the Relations of Parallel Lines Mathematics

Given that ๐ด๐ธ๐น๐ท is a parallelogram, where ๐ธ and ๐น are the midpoints of ๐ท๐ต and ๐ท๐ถ, respectively, find the length of ๐ถ๐ต.

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### Video Transcript

Given that ๐ด๐ธ๐น๐ท is a parallelogram, where ๐ธ and ๐น are the midpoints of ๐ท๐ต and ๐ท๐ถ, respectively, find the length of ๐ถ๐ต.

So our goal is to find the length of ๐ถ๐ต. So letโs begin going through what weโre given. We are given that ๐ด๐ธ๐น๐ท is a parallelogram. And we know that ๐ท๐ด is 2.6 centimeters.

Well, in a parallelogram, opposite sides are congruent.

So that means ๐น๐ธ would also be 2.6 centimeters. Next, weโre given information about midpoints. ๐ธ is the midpoint of ๐ท๐ต. And F is the midpoint of ๐ท๐ถ.

The length of a line segment joining the midpoints of two sides of a triangle is equal to half the length of the third side. So if we look at this triangle, triangle ๐ถ๐ท๐ต, we are told the length of the line segment joining the two midpoints on the two sides of the triangle will be half of the length of the third side, side ๐ถ๐ต.

So ๐น๐ธ should be equal to half of ๐ถ๐ต. Well, we know that ๐น๐ธ is equal to 2.6. So to solve for ๐ถ๐ต, we can multiply both sides of the equation by two. And two times 2.6 is 5.2.

Therefore, the length of ๐ถ๐ต will be equal to 5.2 centimeters.