If one of the angles of a triangle is a right angle (measures90°), then the triangle is called a right-angled triangle or simply, a right triangle.

Definition

The altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side. Also, known as the height of the triangle.

Theorems on Right Angled Triangles

A. The Altitude Theorem
The square of the altitude drawn to the hypotenuse of a right angled triangle is equal to the product of the measures of the segments of the hypotenuse.
ΔABC is a right triangle; h is the altitude drawn from C to the hypotenuse; n and m are segments of the hypo tenuous. Hence,

B. Euclid’s Theorem

Euclid (c. 325 BC – 265 BC) – Greek Mathematician considered the “Father of Geometry”. His textbook ‘Elements’ remained a highly influential mathematics teaching book until the late 19th Century and is one of the most widely published books in the world.

In aright triangle with an altitude drawn to the hypotenuse, the square of the length of each leg is equal to the product of the hypotenuse and the length of the adjacent segment in to which the altitude divides the hypotenuse.