The Pythagorean Theorem A2 + B2 = C2

The Pythagorean Theorem Parts of a Right Triangle Hypotenuse Leg A Leg B

The Pythagorean Theorem Diagonals Side Parts of a Rectangle or Square Notice that two right triangles form a rectangle.

The Pythagorean Theorem A right triangle has one angle that measures 90 degrees. A rectangle and square have four sides that all meet at a 90 degree angle.

The Pythagorean Theorem Categorized by angles Right A triangle with one right angle Acute All angles less than 90 Obtuse One angle more than 90

The Pythagorean Theorem Categorized by sides All sides equal (congruent) Equilateral Isosceles Two sides equal (congruent) Scalene No congruent sides

The Pythagorean Theorem Now for the good stuff. The Pythagorean theorem states that the square of the longest side of a right triangle (hypotenuse) is equal to the sum of the squares of the other two sides. A2 + B2 = C2

The Pythagorean Theorem Click to play animation

The Pythagorean Theorem Pythagoras is credited with proving this theorem; however, there is evidence that Babylonian mathematicians used or knew of the formula long before Pythagoras. Big Question What careers or occupations use or could use the Pythagorean Theorem regularly?

The Pythagorean Theorem Pythagorean Triples are three positive integers that, when plugged into the Pythagorean equation, make it true.

The Pythagorean Theorem The numbers 3, 4, and 5 are probably the most common Pythagorean Triple. Any multiples of this combination also make this equation true. (i.e. 6, 8, and 10, etc.)

The Pythagorean Theorem The converse of the Pythagorean Theorem states that if the square of the longest side of a triangle is equal to the squares of the two legs of a triangle, then that triangle is a right triangle.

The Pythagorean Theorem Now we can try a couple! 29 5. 48 55 74 Is this a right triangle? 21 1. 13 5 2. 20 12 65 33 3. no 25 7 56 4. 24

The Pythagorean Theorem A2 + B2 = C2 Now proceed to the worksheet and then the lesson assessment.