1. 4.7 – Square Roots and The Pythagorean Theorem

2. SQUARES and SQUARE ROOTS: Consider the area of a 3'x3' square: A = 3 x 3 A = (3) 2 = 9

3. = 3 or what POSITIVE number you can multiply by itself to result in the answer of 9. 3 is called the SQUARE ROOT of 9 = 3

4. Squares and Square Roots you should know: Estimate the square roots of the following numbers and then use your calculator to compute the actual values: 1) 2) 3) 4) x123456789101112131415 x2x2 149162536496481100121144169196225

5. THE PYTHAGOREAN THEOREM: Pythagoras was a Greek mathematician from 6 th century BC. He discovered a unique relationship between the sides of a right triangle.

6. The sides adjoining the right angle are called the LEGS of the triangle. The side opposite the right angle is called the HYPOTENUSE.

7. Pythagorean Right Triangle Theorem: The sum of the squares of the legs of a right triangle is equal to the SQUARE of the hypotenuse. In symbols: if a and b are the legs and c is the hypotenuse of the right triangle then:

8. Conversely: If the square of the length of one side of a triangle equals the SUM of the squares of the other two sides then the triangle is a RIGHT triangle.

9. Examples: 1.) If the sides of a triangle measure 5, 12, and 13 inches can it be a right triangle? Pythagorean Formula: a 2 + b 2 = c 2 a = subs: + = b = results: + = c = = YES or NO

10. Examples: 1.) Is the triangle that has sides that measure: 1, 1.5, and 2 yards a right triangle? Pythagorean Formula: a 2 + b 2 = c 2 a = subs: + = b = results: + = c = = YES or NO

11. Homework : Section 4.7 pages 253-255 #’s 6-48 EVEN