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

Example 1 Use the Pythagorean theorem to find the missing side. a 2 + b 2 = c = c = c = c 2 √225 = √c 2 15 = c Solution Is this a right triangle? Yes What is the formula we use to solve for each side of a right triangle? a 2 + b 2 = c 2 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 a 2 + b 2 = c = = = 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? a 2 + b 2 = c 2 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 3 A 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? a 2 + b 2 = c 2 a = 17 2 a = 289 a = -64 a = 225 a 2 = 225 √a 2 = √225 a = 15 The 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? a 2 + b 2 = c 2 a = 78 2 a = 6084 a = -900 a = 5184 √a 2 = √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? A 2 + b 2 = c 2 A = 72

Example 5 Which point is the best estimate of Below √67 Above √64 √ 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