Pythagorean Theorem

The Pythagorean Theorem

Objective of the lesson: Students will learn to derive and use the Pythagorean Formula to find the missing sides of a right triangle.

TEKS of the lesson- Geometry 8.C.- The student is expected to derive, extend, and use the Pythagorean Formula.

The Pythagorean Theroem states: In a right triangle, with sides (legs) a and b, and hypotenuse c, then c²=a²+b².

Note: a right triangle is a triangle with one right angle (an angle of 90°). Its hypotenuse is the side opposite the right angle.

We learned an algebraic proof using similar triangles ABC, CBX, and ACX (in the diagram):

Since corresponding parts of similar triangles are proportional, a/x=c/a or a²=cx.

b/(c-x)=c/b or b²=c²-cx or c²=cx+b².

Substituting a² for cx, we get c²=a²+b². Which is what we were trying to prove.

Next we tried some practice problems.

Example 1: If you are given a triangle with legs of length 3 and 4, what is the length of the hypotenuse?

Answer:

 3^2 + 4^2 = x^2

9 + 16 = x^2

25 = x^2

5 = x

The hypotenuse has length 5

I liked this lesson.  I think the Pythagorean theorem is going to be very useful in the future.  I wonder though- does it matter which side I call A and which side I call B?  I think it doesn't, but I just wanted to check.