pythagorean theorem. bell work □ please graph the problem and the answer: 9² + 12² = □ graph...
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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