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 … Now you try it… ? Equals about 10.91cm
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 = c2 then 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