(5 min) Review of selected problems from lesson 8 (no more than 3
(10 min) Introduce the Pythagorean theorem
A right triangle has one 90 degree angle.
The hypotenuse is the longest side of a right triangle
(the one opposite the 90 degree ("right") angle.
Pythagoras was a famous Greek (about 2200 years ago) who discovered
some interesting math. Pythagoras discovered that if you drew
squares on each side of a right triangle, then the biggest square
had the same area as both of the smaller two squares.
The easiest Pythagorean triangle to construct is the [3,4,5] triangle.
Draw the squares of the triangle shown (32 and 42)
and add them up. You get 25. What is the side of the square whose area is
42 = 16
32 = 9
9 + 16 = 25
Here is the general formula for calculating the
Hand out the formulas worksheet, instructing students to put it in
their notebook for reference when they do their homework.
Use the equation now, and plug in the following numbers:
Notice that the hypotenuse is always the longest side. Most
of the time the numbers do not come out nice. This bothered
the Greeks a lot, and they thought that the [3,4,5] triangle
was magic. By the way, if you are ever building a house and
want to get a right angle, carpenters use the [3,4,5]
triangle to construct a right angle.
What if you are given the hypotenuse and only one leg of the
triangle? How can you find the missing side, such as in this
Well, you work the Pythagorean theorem backward, using this
b2 = c2 -
You find 52 and you subtract 42 to get
32 = 9. then you have to take the square root of
your answer (9) to get 3.
(Remainder of class) In-class exercise
Hand out homework as students successfully complete the in-class exercise.