Pythagorean Theorem
See how to use the pythagorean theorem
to find the side of a right triangle.
5 examples and their solutions.
Pythagorean Theorem
Theorem
a2 + b2 = c2
(a + b)2 = 4⋅12ab + c2 - [4]
a2 + 2ab + b2 = 2ab + c2 - [5]
∴ a2 + b2 = c2
[1]
Draw a right triangle like this.
[2]
Use the above right triangle
to make a square like this.
to make a square like this.
[3]
m∠[plane] + m∠[dot] + 90 = 180
So the interior angles of the middle quadrilateral
are all 90°.
So the middle quadrilateral is a square.
So the interior angles of the middle quadrilateral
are all 90°.
So the middle quadrilateral is a square.
[5]
(a + b)2 = a2 + 2ab + b2
Polynomial
Polynomial
Close
Example
Example
x2 + 52 = (√89)2
x2 + 25 = 89
x2 = 64
x = 8
Close
Pythagorean Triples
Definition
3, 4, 5
5, 12, 13
7, 24, 25
...
The Pythagorean triple is three positive integers5, 12, 13
7, 24, 25
...
that satisfy the Pythagorean theorem:
a2 + b2 = c2.
In high school,
these triples (and their multiples) are mostly used.
Example
x = 3
(x, 4, 5)
→ (3, 4, 5)
→ x = 3
→ (3, 4, 5)
→ x = 3
Close
Example
x = 13
(5, 12, x)
→ (5, 12, 13)
→ x = 13
→ (5, 12, 13)
→ x = 13
Close
Example
x4 = 63 - [2]
x4 = 2
x = 8
[1]
(6, x, 10)
→ ×2 of (3, 4, 5)
→ So draw (3, 4, 5) right triangle
next to the given triangle.
→ ×2 of (3, 4, 5)
→ So draw (3, 4, 5) right triangle
next to the given triangle.
[2]
Close