# Today in Triangle Appreciation

As it’s 10/12/10, I thought it would be the appropriate day to appreciate the 10-10-12 triangle!

Of course, it’s nice that the 10-10-12 triangle is isosceles.  But what’s really cool is what happens when you drop the altitude from the top vertex!

It’s well known that in an isosceles triangle, the median and the altitude from the vertex are the same–this means that not only does this segment make a right angle (it’s the altitude), but it also divides the opposite side at its midpoint (it’s the median).  So that segment creates two right triangles with hypotenuse 10 and side 6.  Of course, the other side must be eight, since

$6^2 + 8^2 = 10^2$

Thank you, Pythagorean Theorem.  So the 10-10-12 triangle is just two right triangles pasted together.

It’s not quite equilateral, but the 10-10-12 triangle is still pretty cool.

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Categories: Geometry

#### patrick honner

Math teacher in Brooklyn, New York

#### Alan · October 13, 2010 at 1:10 am

I remember this triangle from this morning. 😛 A Facebook plugin, experimenting with plugins?

Well, are there any other “special” days to be on the look out with this same “format” ?

10/12/10 -> 8/10/8? Altitude of 6?

3/4/5
6/8/10
10/10/12 -> 2012?
9/12/15
12/16/20

#### Simon Gregg · May 25, 2013 at 2:59 pm

– and it’s a Heronian triangle – with an inradius of exactly 3!

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