A right-angled triangle is a triangle which has a right-angle. If we know the length of two edges of a right-angled triangle, we can find out the length of the third edge. We need to use Pythagorean theorem.
Hypotenuse of a triangleIn a right-angled triangle, the largest edge is called the hypotenuse.
Pythagorean theoremIn a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the two other edges.
In an problem, if you are asked to show that a triangle is a right-angled triangle and you know the length of the three edges, then you must use the reciprocal of Pythagorean theorem.
Examples of the use of the theorem :
Reciprocal of Pythagorean theoremIf in a triangle, the length of the largest edge is equal to the sum of the squares of the two other edge, then this triangle is a right-angled triangle.
To show that the triangle ABC is right-angled, we calculate separately and .
, therefore, according to the reciprocal of Pythagorean theorem, the triangle ABC is right-angled at B.