The Pythagorean Theorem

1. The Pythagorean Theorem By: Ekjot, Banita, and Skyla

2. It states… If we let a and b be the lengths of the form the right angle and let c be the length of the hypotenuse, then the following relation holds: a2 + b2 = c2

3. Now you try if it works… ? Equals 10 cm

4. It also states … If a2 + b2 = c2 , then c2 – b2 = a2 or c2 – a2 = b2 Now you try it… ? Equals about 10.91cm

5. The converse of the Pythagorean Theorem When the following relation holds among the lengths of the three sides a, b, and c of a triangle, a2 + b2 = c2then it is a right triangle, and with a length of c is the hypotenuse. Our assumption is in triangle ABC where line BC = a, line AC = b and line AB = c, and where a2 + b2 = c2 our conclusion would be angle c = 90 degrees.

6. Now you try if it works… Which ones of the following lengths could be the lengths of a right angle triangle? Lengths: 8cm, 15cm, 17cm Yes, it is a right angle triangle Lengths: 75cm, 23cm, 71cm No, it isn’t a right angle triangle

7. Using the Pythagorean Theorem Find the length of the wire Length of the wire = 20 ft.

8. Diagonals of a square… Looking at the square on the left: a2 + a2 = d2 2a2 = d2 / Square root Square root of 2a2 = d a d Square root of 2 x a = d a

9. Now you try if it works… Find X (Round it to 2 decimal places) Q X equals about 4.24 5 S P 4 R

10. Height of an Equilateral Triangle Formula: a2- (a2 / 22)= h2 Also written as (when simplified): (Square root of 3/2) x a = h

11. Now you try it… Find h (round it to 2 decimals places). h equals about 4.33 5cm h

12. Area of an Equilateral Triangle Formula: (Square root of 3 / 4) x a2 = Area Now you try it …..Find the Area of the triangle on the left. Area Equals about 2.71cm