Pythagorean Theorem Notes Absent Copy 3/11,12

1. Pythagorean TheoremNotesAbsent Copy3/11,12

2. Pythagorean Theorem a2 + b2 = c2Leg + Leg = Hypotenuse (longest side) 25 sq ft. 5 c 3 9 sq ft. A B 4 16 sq ft.

3. Example 1 • Use the Pythagorean theorem to find the missing side. a2 + b2 = c2 92 + 122 = c2 81 + 144 = c2 225 = c2 √225 = √c2 15 = c Solution • Is this a right triangle? Yes • What is the formula we use to solve for each side of a right triangle? • a2 + b2 = c2 • What is another name for the longest side “c”? • The Hypotenuse • After substituting the #’s and making an equation what do we do we do first? • We use GEMA and start with exponents. Then we add the like terms. • What inverse Op. do we use? • We use the inverse of exponents which is to square root both sides of = sign. 15

4. Example 2 • Tell whether the given lengths form a right triangle. 5, 6, 11 a2 + b2 = c2 52 + 62 = 112 25 + 36 = 121 61 = 121 Both sides are not = Solution • Which # do you think will be the hypotenuse? Why is this important? • The 11 will be the hypotenuse because it is the largest # which goes with the longest side. • Does it matter what # we substitute for a and b? No it doesn’t really matter what # is substituted for A or B • What is the formula for a right triangle? • a2 + b2 = c2 • After substituting the #’s into the formula what do we do first? • We use GEMA and work out all the exponents. • What do we do next? • We add like terms and see if each side = each other. • Do these #’s make a right triangle? • NO both sides are not equal. Not a Rt triangle

5. Example 3A ladder is placed against a vertical wall of a building. The bottom end of the ladder is 8 ft. from the base of the building and the length of the ladder is 17 ft. How high up the side of the building is the ladder leaning?a2+ b2 = c2 a2 + 82 = 172a2+ 64 = 289a2-64 = -64a2 + 0 = 225a2 = 225 √a2 = √225a = 15The ladder is leaning 15 ft. off the ground building