Medians on a Trapezoid: Geometry

Greeting math peeps! Welcome to another MathSux post! Today we will be tackling how to find the missing lengths of medians on a trapezoid. We’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 it’s not so hard; you just have to know what to do.Let’s take a look:

Medians on a Trapezoid

How do I answer this Question?

Step 1: Let’s fill in what we know, They tell us in the questions that AB=5x-9, DC=x+3, and EF=2x+2. So let’s write that in:

Medians on a Trapezoid

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 didn’t know about (Exciting I know).

Screen Shot 2016-08-08 at 11.19.28 AM

Step 2: Apply the rule and solve for x.

Medians on a Trapezoid

Answer: x=5

Yay! This gives us our answer 🙂 Another random rule in Geometry accomplished.

 Still got questions? That’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!

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6 thoughts on “Medians on a Trapezoid: Geometry”

  1. 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.

    1. I took geometry in highschool but don’t even remember this. There are so many things to remember in this subject and if you don’t use it on a daily basis it’s so easy to forget. Glad you enjoyed this post! 🙂

  2. I didn’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 – draw lines straight down from C,D,E and F.)

    This gives us:


    Taking the first equation from the second gives:


    Now we can solve for x.

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