1. The Pythagorean Theorem
Tutorial 12d

2. The Pythagorean Theorem
In a right triangle, the side opposite the right angle is the longest side. It is the hypotenuse.
The other two sides are the legs of a right triangle.
Side c is the hypotenuse, and is the longest side. c a
Sides a and b are the legs of the triangle. b

3. a2 + b2 = c2 32 + 42 = 52 Pythagorean Theorem
In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
a2 + b2 = c2 c =5 a =3
Example:
= 52 b =4

4. Example #1 c c c 1. 2. 3. 100m 70m 18in 35ft 68ft 34in a2 + b2 = c2

5. Example #2 a2 + b2 = c2 x2 + 42 = 62 x2 + 16 = 36 -16 -16 x2 = 20
Find the value of the variable. Round your answers to the nearest tenth.
a2 + b2 = c2
x = 62
x = 36
x2 = 20
a2 + b2 = c2
102 + y2 = 142
100 + y2 = 196
y2 = 96
a2 + b2 = c2
92 + p2 = 102
81+ p2 = 100
p2 = 19
x  4.5
y  9.8
p  4.4

6. Pythagorean Theorem
When the lengths of the sides of a right triangle are integers, the integers form a Pythagorean triple.
Example:
= 52
= 25 5 3
25 = 25 4
The numbers 3, 4, & 5 are called Pythagorean Triples

7. The Converse of the Pythagorean Theorem
If the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
Is this triangle a right triangle?
= 102 10 6
= 100
100 = 100 8
Yes it is a right triangle

8. Are the following triangles right triangles?
More Examples
Are the following triangles right triangles? 1. 2. 3.
? 8.52
? 172
? 212 ?
? 289
? 441 ? =
274 ? 289 
468 ? 441 
Yes,
it is a right triangle
No,
it is not a right triangle
No,
it is not a right triangle

9. The End
Time to move on
to the assignment or
the next lesson