Math 9 Notes - Pythagorean Theorem PDF

## Math 9 Quiz #1 - Number Sets - Rational/Irrational - Perfect Squares ### Pythagorean Theorem - Used to solve unknown side on a right-angled triangle. ![A right triangle containing the side lengths of a, b, and c. The angle opposite side c is marked as 90 degrees.] - Be sure to label your tri...

## Math 9 Quiz #1 - Number Sets - Rational/Irrational - Perfect Squares ### Pythagorean Theorem - Used to solve unknown side on a right-angled triangle. ![A right triangle containing the side lengths of a, b, and c. The angle opposite side c is marked as 90 degrees.] - Be sure to label your triangle correctly. - The hypotenuse will always be the longest side. - The hypotenuse will always be opposite your right angle. - The legs are the sides a and b. - The legs are the sides that make the right angle. - $a^2 + b^2 = c^2$ - The sum of the squares of the legs will equal the square of the hypotenuse. ### Trades Note - Draw out 3 inches and draw out 4 inches then measure the hypotenuse. - $c^2 = a^2 + b^2$ - $c = \sqrt{a^2 + b^2}$ - Solve for c. - Example: solve for a - $c^2 = a^2 + b^2$ - $c^2 - b^2 = a^2$ - $a = \sqrt{c^2 - b^2}$ ### Remember: - The square root of perfect squares are rational numbers. - Why? $\sqrt{16} = \sqrt{4 \times 4} = \sqrt{4^2} = 4$ - Now we will look at non perfect squares, which are irrational numbers. - For example, $\sqrt{5}$ is irrational because no two equal rational numbers multiply out to 5. - We can however, use a calculator to find a decimal approximation of these values. #### Example - Find the decimal approximation of $\sqrt{12}$ - No two rational numbers multiply out to $\sqrt{12}$ - By calculator $\sqrt{12} = 3.464...$, which is irrational. - So: Round to two decimal places. $\sqrt{12} = 3.46$ ##### Rules of Rounding - 4 or less - leave be - 5 or more - round up ###### Example: - Round to 2 decimal places - 4.6178 to 4.62 - The number **after** the "cut-off" determines rounding. - 1.1214 to 1.12 - Approximating without a calculator - Example: Find the decimal approximation of the square root of $\sqrt{11}$ without a calculator. - We know: - $\sqrt{11}$ is not a whole number. - Its value lies between 9 and 16. - The solution must then lie between 3 and 4. - $\sqrt{11}$ is 2 units from 9 and 5 units from 16. - $\sqrt{11}$ is closer to 9. - Guess: 3.3^2 = 10.89