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Pythagorean Theorem Notes Absent Copy 5/19. Pythagorean Theorem a 2 + b 2 = c 2 Leg + Leg = Hypotenuse ( longest side ) . Leg called A or B. Leg called C or Hypotenuse. Leg called A or B. Example 1. Use the Pythagorean theorem to find the missing side.

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## Pythagorean Theorem Notes Absent Copy 5/19

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**Pythagorean Theorem a2 + b2 = c2Leg + Leg =**Hypotenuse (longest side) Leg called A or B Leg called C or Hypotenuse Leg called A or B**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**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**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**Different Shapes W/Pythagorean Theorem**Rectangle • Diagonal is the line that cuts diagonally through a rectangle or square. • How many Rt triangles are there?**Example 4**• The diagonal of a rectangle parking lot is 78 in. The width of the parking lot is 30 in. What is the length of the parking lot? a2 + b2 = c2 a2 + 302 = 782 a2 + 900 = 6084 a2+ -900 = -900 a2 + 0 = 5184 √a2 = √5184 a = 72 • What letter is the Hypotenuse? A or B or C • What does it mean when two lines are perpendicular? • Its means they intersect each other. • What are we trying to solve for? • We are trying to find the length of the parking lot. • How do we set up equation? • A2 + b2 = c2 A = 72**Example 5**• Which point is the best estimate of . 8 8.2 8.4 8.6 8.8 9 Below√67 Above √64 √81 8 8.2 9 • What do we do first to find the sq. rt. Of this non-perfect square? • We find the below and above perfect square. • What do we do next? • Draw a # line and make an estimate. • Which point is the sq. rt. of closer too? • It is closer to 8.2 on the number line. √67 = 8.2

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