Pythagorean Theorem

Bell Work□Please graph the problem and the answer: 9² + 12² =

□Graph the problem on one paper and the answer on the other paper. See my Example on the board.

Pythagorean Theorem -

□In right triangles, the square of the length of the hypotenuse is equal to the sum of the squares of its legs.

□a² + b² = c²

Right Triangle□right triangle –triangle that has one

right angle □leg – the two sides of a right triangle

that form a right angle□right angle – an angle that measures

90º□hypotenuse – the side of a right

triangle that is opposite the right angle; the longest side of a right triangle

hypotenuseleg

leg

right angle

90°

Who can find the Right Triangles?

Is the triangle Right?Using the Pythagorean Theorem,

determine which of the following would be right triangle.

a.18 feet, 24 feet, 30 feetb.3 miles, 4 miles, 5 milesc.11 inches, 13 inches, 17 inches

Converse□If you reverse the parts of the

Pythagorean Theorem, you have formed its converse. The converse of the Pythagorean Theorem is also true.

□EX: c² = a² + b²□if the sides of a triangle have lengths

a, b and c so that c² = a² + b², then the triangle is a right triangle.

Example:□The hypotenuse of a right triangle is 15 feet and leg a is 12 feet. What is the length of leg b?

Pythagorean Triples

□A set of three integers that satisfy the Pythagorean Theorem.a b c Check a² + b² =

c²

original

3 4 5 9 + 16 = 25

x2 6 8 10 36 + 64 = 100

x3 9 12 15 81 + 144 = 225

x4 12 16 20 144 + 256 = 400

x5 15 20 25 225 + 400 = 625

Who uses the Pythagorean

Theorem?□Cartographers (map makers)

□Surveyors□Designers□Architects□Pilots

□Sailors□Astronomers□Astronauts□Construction Workers

□Oceanographers

Do I use the Pythagorean

Theorem?□Which path is the quickest?

1 mile

2 miles

2 miles

1 mile