Pythagoras Theorem

Topic Content:

From the geometrical point of view, Pythagoras theorem gives the relation between areas of squares on the sides of a right-angled triangle. Also, from an algebraic point of view, the formula below can be used to solve right-angled triangles.

If squares are drawn on each side of a right triangle, the area of the square on the hypotenuse equals the sum of the areas of the squares on the other two sides

⇒ \( \scriptsize a^2 = b^2 \: + \: c^2\)

which is \( \scriptsize Hyp^2 = Opp^2 \: + \: Adj^2\)

 Pythagorean Triple:

In ΔABC above, the sides are 3 cm, 4 cm and 5 cm. This is an example of a Pythagorean triple, i.e. a set of 3 whole numbers which can be taken as the lengths of the sides.

\( \scriptsize 5^2 = 4^2 \: + \: 3^2\)

\( \scriptsize 25 = 16 \: + \: 9\)

\( \scriptsize 25 = 25\)

When a triangle’s sides are a Pythagorean Triple it is a right-angled triangle.

Another example is 5, 12, 13

\( \scriptsize 13^2 = 5^2 \: + \: 12^2\)

\( \scriptsize 169 = 25 \: + \: 144\)

\( \scriptsize 169 = 169\)

Here is a list of pythagorean triples

Example 4.2.1:

If the diagonal of a square is 8 cm, what