Greeting math peeps! Welcome to another MathSux post! Today we will be tackling how to find the missing lengths of medians on a trapezoid. Weâ€™ll do this by going over a question taken straight from the NYS Regents from August 2012. I must admit, that when I first looked at this question, I had no idea how to answer it! None. Zero. Clueless (also a great movie). But apparently, there is an explanation! And apparently itâ€™s not so hard; you just have to know what to do.Letâ€™s take a look:

## How do I answer this Question?

**Step 1:** Letâ€™s fill in what we know, They tell us in the questions that AB=5x-9, DC=x+3, and EF=2x+2. So letâ€™s write that in:

Ok, great what now? (This is where I got lost too). But wait! There is this amazing rule about medians on a trapezoid you probably didnâ€™t know about (Exciting I know).

**Step 2:** Apply the rule and solve for x.

**Answer**: x=5

Yay! This gives us our answer đź™‚ Another random rule in Geometry accomplished.

Â Still got questions? Thatâ€™s cool, take a deep breath and ask me in the comments section.

Looking for more on Medians of a trapezoid? Check out this post here for practice questions and more!

To be honest, I never learned this in my high school (in Ontario, Canada). We had up to grade 13 in high school and Geometry before I entered high school. At my time they took out grade 13 and Geometry.

So this is why this is new to me. I think Geometry should make a comeback to increase demand for good architects to make fancy looking buildings/houses/theme parks, etc.

Now I know this. Thank you.

I took geometry in highschool but donâ€™t even remember this. There are so many things to remember in this subject and if you donâ€™t use it on a daily basis itâ€™s so easy to forget. Glad you enjoyed this post! đź™‚

I didnâ€™t know the result you used. Here is how I thought about it:

Say EF is longer than DC by some amount L.

Notice that AB is longer than EF by the same amount L.

(You can see this by drawing triangles â€“ draw lines straight down from C,D,E and F.)

This gives us:

2x+2=x+3+L,

5x-9=2x+2+L.

Taking the first equation from the second gives:

3x-11=x-1.

Now we can solve for x.

I never would have thought of thatâ€¦thatâ€™s awesome! It makes a lot more sense than a random rule too. đź™‚