WARM UP Decide whether the set of numbers can represent the side lengths of a triangle. 2, 10, 12 6, 8, 10 5, 6, 11

The Pythagorean Theorem and Its Converse Geometry

PYTHAGOREAN THEOREM In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

PYTHAGOREAN TRIPLE A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation c2 = a2+ b2.

Common Pythagorean Triples 3, 4, 5 5, 12, 13 7, 24, 25 9, 40, 41 11, 60, 61 We can multiply these by a common factor to get more…. 6, 8, 10 10, 24, 26 14, 48, 50 18, 80, 82 22, 120, 122

Finding the Hypotenuse Find the length of the hypotenuse of the right triangle.

Finding the Leg Find the length of the leg of the right triangle.

Find the Area

Example Damon is locked out of his house. The only open window is on the second floor, which is 12 feet above the ground. He needs to borrow a ladder from his neighbor. If he must place the ladder 5 feet from the house to avoid some bushes, what length of ladder does Damon need?

CONVERSE OF THE PYTHAGOREAN THEOREM If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. If c2 = a2 + b 2 , then triangle ABC is a right triangle

How do you know which side to use as c?

What if it is not a right triangle?

Always make sure it is a triangle before checking what kind!!

Once we know it is a triangle… Use the longest side as c and figure out what type of triangle it is.

Examples Decide whether the set of numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse. a. 8, 18, 24 b. 3.2, 4.8, 5.1 c. 5, 7, 13 d. 12.3, 16.4, 20.5