Video Transcript
Using the information in the
figure, determine the length of line segment 𝐸𝐹.
First, we’ll identify line segment
𝐸𝐹. And then we’ll think about what we
already know based on the figure. We see in our figure that we have
three parallel lines. And so we can say that 𝐴𝐷 is
parallel to 𝐸𝐵, which is parallel to 𝐹𝐶. Then we can say that the lines 𝐷𝐹
and 𝐴𝐶 are transversals of the three parallel lines. Because we have three parallel
lines being cut by two transversals, we know that the created segments are cut
proportionally, by the properties of parallel lines and transversals.
This means we can say that 𝐷𝐸
over 𝐸𝐹 will be equal to 𝐴𝐵 over 𝐵𝐶. If we plug in the lengths we do
know, we have 48 over 𝐸𝐹 is equal to 47 over 141. To solve, we cross multiply. 48 times 141 will be equal to 47
times 𝐸𝐹. Therefore, 6768 is equal to 47
times 𝐸𝐹. And dividing both sides by 47 gives
us 144 is equal to 𝐸𝐹. Since our segments are measured in
centimeters, we can say that 𝐸𝐹 is equal to 144 centimeters.
