6.1 Pythagoras’ Theorem
6.1.1 Pythagoras’ Theorem
1. In a rightangled triangle, the hypotenuse is the longest side of the triangle.
2. Pythagoras’ Theorem:
In a rightangled triangle, the square
of the hypotenuse is equal to the sum
of the squares of the other two sides.

Example 1:
Solution:
$\begin{array}{l}{x}^{2}={5}^{2}+{12}^{2}\\ \text{}=25+144\\ \text{}x=\sqrt{169}\\ \text{}=13\end{array}$
Example 2:
Solution:
$\begin{array}{l}{x}^{2}={15}^{2}{9}^{2}\\ \text{}=22581\\ \text{}x=\sqrt{144}\\ \text{}=12\end{array}$
3. Pythagorean triples are three whole numbers that form the sides of a rightangled triangle.
Example:
(a) 3, 4, 5
(b) 6, 8, 10
(b) 6, 8, 10
(c) 5, 12, 13
(d) 8, 15, 17
(d) 8, 15, 17
(e) 9, 12, 15
6.1.2 The Converse of the Pythagoras’ Theorem
In a triangle, if the sum of the squares of the two sides
is equal to the square of the longest side, then the angle
opposite the longest side is a right angle.
