Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

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Recall that a **triangle midsegment** is half of the length of the side of a triangle it is parallel to. Knowing this, if the length of the midsegment is given in terms of a variable, it is possible to solve for the variable.

Set the expression for the length of the midsegment equal to half of the length of the side it is parallel to. For example, if the side it is parallel has a length of 24, set the midsegment's expression equal to 24/2 = 12. Then, using algebra, solve for the unknown variable.

You can use what you know about triangle midsegments to find the values of missing variables. So first I’ll start off by saying what do we know about triangle midsegments? Well we know that if I am giving you a triangle midsegment it’s going to be half the length of the side that it’s parallel to, also known as the third side. So let’s go back to our problem.

We have two variables that we’re looking for x and y and we have 3 times x is the length of that mid-segment. So the side that it’s parallel to is the side that says it’s 48, so I’m going to mark these two lines or line segments as being parallel. And I’m going to write an equation that says 3x is equal to not 48, but half of 48. So I can solve this equation for x. Well half of 48 is 24, so 3x equals 24 and I’m going to divide by 3 and I find out that x must be 8. So the key thing there was realizing that 3x is not equal to 48, but it’s equal to half of 48 which is 24.

Let’s use the same mentality to find y. Well we can write that, I’m going to move down here a little bit, so we can write there y plus 2 is equal to half of its parallel side. So this side y plus 2 is parallel to 20, so y plus 2 is equal to half of 20. So to solve this I’m going to do half of 20 is 10, so y plus 2 equals 10 and the last step I’m going to subtract 2 and I find y must be 8.

So the key thing to this problem is remembering that your midsegment will be half of the side that it’s parallel to.