Right-Angled Triangles and Pythagoras Property A right-angled triangle is a triangle where one of the angles measures exactly 90°. This means that the op...
A right-angled triangle is a triangle where one of the angles measures exactly 90°. This means that the opposite and adjacent angles also measure 90°.
The Pythagoras theorem states that in any right-angled triangle, the square length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. This means that:
Hypotenuse^2 = Opposite^2 + Adjacent^2
Example:
In the following triangle:
The hypotenuse is 10 cm.
The opposite side is 6 cm.
The adjacent side is 8 cm.
According to the Pythagorean theorem, 10^2 = 6^2 + 8^2, which holds true, confirming that the theorem is applicable.
The Pythagoras property is a powerful tool that can be applied to solve various problems involving right-angled triangles. By using the theorem, we can easily find the lengths of the other two sides given the lengths of the hypotenuse and one of the other sides