501 Geometry Questions

Pythagorean Theorem

The Pythagorean theoremis used when you know the lengths of two sides
of a right triangle and want to find the length of the missing third side. This
can be done when the two given lengths are the legs, or when you know the
length of the hypotenuse and one of the legs. What is most important to
remember, is that in your equation, the hypotenuse is alwaysthe side that
begins all alone. Here’s the formula:

(length of leg #1)^2 + (length of leg #2)^2 = (length of hypotenuse)^2

Since it is standard to label the sides of the triangle as a, b, and cas in the
previous figure, the Pythagorean theorem is more commonly known as:

a^2 + b^2 = c^2

A note on exponents!If you are not familiar with the small “2” that is above
and to the right of each letter, this is an exponent. “a^2 ” does not mean a times
two, but it means atimes itself two times. Therefore, “x^3 ” would mean xtimes
itself threetimes and notxtimes three. To undo an exponent, you need to
take the square root of a number, which means discovering what number
multiplied by itself two times gives that answer. The symbol for the square
root looks like  10 . Therefore, x^2 =  64 means what number, multiplied
by itself two times, yields 64. (The answer is 8, since  64 = 8).

Look carefully over the following three examples to see how the
Pythagorean theorem is used with right triangles:

Example 1: Find hypotenuse QR.

a = 3

b = 4

c =?

Q

S

R

501 Geometry Questions