1. The Pythagorean Theorem
A2 + B2 = C2

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

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

4. 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.

5. 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

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

7. 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

8. The Pythagorean Theorem
Click to play
animation

9. 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?

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

11. 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.)

12. 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.

13. 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

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