Question Video: Using the Properties of Parallel Lines to Solve a Problem Mathematics

Using the information in the figure, determine the length of 𝐸𝐹.


Video Transcript

Using the information in the figure, determine the length of line segment 𝐸𝐹.

First of all, we can identify line segment 𝐸𝐹. And then we need to think about what we know based on the figure. In the figure, we have three parallel lines. Line 𝐴𝐷 is parallel to line 𝐸𝐡, which is parallel to line 𝐹𝐢. We can also say that lines 𝐷𝐹 and 𝐴𝐢 are transversals of the three parallel lines. Based on this, we know that the parallel lines are going to cut the transversals proportionally. This means that line segment 𝐷𝐸 over line segment 𝐴𝐡 will be equal to line segment 𝐸𝐹 over line segment 𝐡𝐢 because of the parallel lines and transversal properties. Once we have this statement, we can just plug in the values for the three line segments we know and use that information to solve for the fourth line segment, which will look like this. 48 over 47 is equal to 𝐸𝐹 over 141.

From there, we cross multiply. 141 times 48 must be equal to 47 times 𝐸𝐹. 6768 is equal to 47 𝐸𝐹. And then we divide both sides of this equation by 47, which tells us that 144 is equal to 𝐸𝐹. And so we can say that line segment 𝐸𝐹 must measure 144 centimeters.

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