Ruler and Compass Construction: Perpendicular Bisector

I started the ruler and compass series a while ago and am just now getting back to it. Here is my construction of a perpendicular bisector of a given line segment.

First, I drew a line segment:

Using my compass (which quickly gave out on me), I made two big fat arcs. They have the same radius – this is important.

Where those two cross, I drew a line. That line is the perpendicular (at 90 degree angle to) bisector (splits in in two equal pieces) of the original segment:

Why does it work?

Well, that’s a great question. I’m sure there’s some proof of why this actually results in splitting the original line segment in half with a perpendicular line. I’ll have to think on it more.

But intuitively it totally feels right.

Now that’s a bad way to proceed with math, but it’s a great first start!

How about you?

Do you like to play with ruler and compass constructions? Do you know why this works?

Oh – and if you don’t have one, buy a compass here (that’s the one I just bought to replace my junky one).

And I also ordered this cool book about Compass Drawings – I’m so excited!

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6 Responses to Ruler and Compass Construction: Perpendicular Bisector

  1. Vijay says:

    Lovely stuff cousin, reminded me of my Math education which I did some 25 years ago.

    Take care

    Vijay

  2. T. says:

    Bon, sometimes you scare me. I just received my copy of *this same* book two days ago. It is, along with Cartooning with Math (also one of your suggestions), meant to keep the Kindergartener (and myself) busy on a flight to grandparents. She declared after a quick assessment of the books, “very cool, Mom”!

  3. T. says:

    Also, we’re using the Safe-T compass and protractor/straight edge set.

    • Bon says:

      I think I got the “watch it or this could turn into a murder weapon one.” And with my clumsiness, you might watch for me on the news.

      #fingerscrossedIdontputoutaneye

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