If 𝐵𝐴 equals 24 centimetres and 𝐷𝐶 equals 26 centimetres, find the length of line segment 𝐾𝐹.
Let’s start this question by having a look at the diagram. We can see that we have an outer quadrilateral 𝐶𝐷𝐴𝐵. But which particular quadrilateral is it? Well, we can see from the diagram that it has a pair of parallel sides. And as it doesn’t have any 90-degree angles marked, then we could say that 𝐶𝐷𝐴𝐵 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 𝐶𝐷𝐴𝐵.
The question is asking us to find the length of line segment 𝐾𝐹. We can see in our diagram that line segment 𝐶𝐾 is equal to line segment 𝐵𝐾, which means that 𝐾 must be the midpoint of line segment 𝐶𝐵. On the other side of our trapezoid, we can see that the line segment 𝐷𝐹 is equal to the line segment 𝐴𝐹. Therefore, 𝐹 must be the midpoint of line segment 𝐷𝐴. So, if we look at our line segment 𝐾𝐹, 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 𝐾𝐹, we’ll have our length 𝐷𝐶 plus the length of 𝐵𝐴. And we find half of that answer. We’re given that the length of 𝐷𝐶 is 26 centimetres. And we add our value for 𝐵𝐴, 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 𝐾𝐹 is 25 centimetres.