### Video Transcript

If π΅π΄ equals 24 centimetres and π·πΆ equals 26 centimetres, find the length of line segment πΎπΉ.

Letβs start this question by having a look at the diagram. We can see that we have an outer quadrilateral πΆπ·π΄π΅. But which particular quadrilateral is it? Well, we can see from the diagram that it has a pair of parallel sides. And as it doesnβt have any 90-degree angles marked, then we could say that πΆπ·π΄π΅ must be a trapezoid. It can be easy to think that a trapezoid must always look in the way we usually see them, with a larger base at the bottom. But since it just has to have a pair of parallel sides, then this is what we have with πΆπ·π΄π΅.

The question is asking us to find the length of line segment πΎπΉ. We can see in our diagram that line segment πΆπΎ is equal to line segment π΅πΎ, which means that πΎ must be the midpoint of line segment πΆπ΅. On the other side of our trapezoid, we can see that the line segment π·πΉ is equal to the line segment π΄πΉ. Therefore, πΉ must be the midpoint of line segment π·π΄. So, if we look at our line segment πΎπΉ, then we can say that this must be the midsegment of our trapezoid since the midsegment of a trapezoid is the segment connecting the mid points of the two nonparallel sides.

We can find the length of the mid segment by taking half the sum of the lengths of the two parallel sides. So, to find our line segment πΎπΉ, weβll have our length π·πΆ plus the length of π΅π΄. And we find half of that answer. Weβre given that the length of π·πΆ is 26 centimetres. And we add our value for π΅π΄, which is 24 centimetres, and divide by two. Adding our 26 and 24 will give us 50. And 50 over two is 25. And so, our answer, including the units, for line segment πΎπΉ is 25 centimetres.