Wednesday, November 14, 2012

Angle Chasing Shortcut #1

This nifty little diagram is of a triangle with angles a, b, and c.  The exterior angles are marked a+b and a+c because they equal the sum of angles a and b, or however they are written out.

A simple proof of this is that since that the "sum angle" has to be a, b, or c minus 180˚, reason being that a line has an angle of 180˚ so the missing "sum angle" has to be the difference of the given angle and 180˚.  Since the "sum angle"+b=180 and a+c=180, the "sum angle" has to be a+c or the other two angles.

I posted a slightly less complex version of the first image on the "Geometry Web" in the classroom without a proof just so nobody has a panic attack because they can't figure out why this is true. This diagram is useful for angle chasing because it allows us to skip over some angles that aren't necessary to solve, and we can all agree that addition is less time consuming than subtraction, so once applied to the sheet, you will just breeze through them at like 2 minutes per sheet or something really fast.

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