The Pythagorean Theorem
The Pythagorean Theorem is one of the most fundamental principles in geometry. It applies to
right-angled triangles.
Theorem Statement:
In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right
angle) is equal to the sum of the squares of the other two sides.
This can be written as:
a^2 + b^2 = c^2
Where:
a and b are the lengths of the two shorter sides (legs)
c is the length of the hypotenuse
Example:
Suppose we have a right-angled triangle where:
a = 3 cm
b = 4 cm
Then, to find the hypotenuse c:
a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
Page 1
The Pythagorean Theorem is one of the most fundamental principles in geometry. It applies to
right-angled triangles.
Theorem Statement:
In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right
angle) is equal to the sum of the squares of the other two sides.
This can be written as:
a^2 + b^2 = c^2
Where:
a and b are the lengths of the two shorter sides (legs)
c is the length of the hypotenuse
Example:
Suppose we have a right-angled triangle where:
a = 3 cm
b = 4 cm
Then, to find the hypotenuse c:
a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
Page 1
