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3

I really wish people would stop teaching the Pythagorean Theorem as $a^2 + b^2 = c^2$, for the following reason: Give your students the diagram below, and ask them to solve for $c$. At least 1/3 of a typical high school class will write $a^2 + b^2 = c^2$ and report back to you that $c = 5$. The problem is that the equation $a^2 + b^2 = c^2$ is so ...


3

Whatever you choose, make sure to follow some basic rules: Clearly state the preconditions and make sure they are understood (right triangle in your case). Clearly state the meaning of the symbols (e.g. which symbols stand for the sides adjacent to the right angle, and which for the third one). Use the symbols consistently (don't make e.g. the same symbol &...


8

Two alternatives I have seen used (am not necessarily recommending them, but will list some pros and cons) which don't seem to have been mentioned yet. Don't denote it algebraically at all! Draw a picture instead For the lower end of the 12-16 age range, I've seen this work really well. You literally draw the squares sticking out from the triangle. Write the ...


10

In Olympiad geometry, $a$, $b$, $c$ is the so-called standard notation for the sides of a triangle, so it makes sense to use it consistently when referring to a triangle (in isolation). However, in any case the general principle is introducing all your notation. Writing Pythagoras' theorem states that $a^2+b^2=c^2$. or Pythagoras' theorem states that $...


-2

I prefer to state it the traditional way, not involving multiplying a length by itself, but involving areas of those polygons known as squares. Draw two lines at right angles to the hypotenuse at its two endpoints to get two sides of the square other than the hypotenuse itself, and draw the fourth side, and there you have a square, whose area is the sum of ...


19

Common knowledge The formula $a^2+b^2 = c^2$ is common knowledge and the words for hypotenuse and leg (is "cathetus" not used in English?) are basic mathematical vocabulary. Including these seems a good idea. Connections to other mathematics The notation with AB, CA and BC might be something the students have used or will use in less analytical ...


6

The only one of these that looks objectionable to me is the one that calls the hypotenuse $h$, since in a triangle the letter $h$ usually refers to the triangle's height (which could be either one of the legs but could not be the hypotenuse).


1

I remember getting my first 18 inch slide ruler. I had worked hard, poison oak filled, hours making fire breaks in the Oakland hills to make enough money to get it. It was aluminum, had a spring loaded cursor that slid like it was greased, and the C and D scales (I think) lined up perfectly. It was huge and had scales I was never going to use. I loved it. ...


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