CAT Pythagoras Theorem - Practice Questions & MCQ

This theorem was earlier given by an ancient Indian mathematician Baudhayan (about 800 B.C.E.) in the following form :

The diagonal of a rectangle produces by itself the same area as produced by its both sides (i.e., length and breadth). For this reason, this theorem is sometimes also referred to as the Baudhayan Theorem.

Theorem : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given: 

To Prove: 

Construction: 

Proof: In and , we have

In and , we have

The converse of Pythagoras Theorem

In a triangle, if the square of one side is equal to the sum of the squares of the other two sides then the angle opposite to the first side is a right angle.

Given: 

To Prove: 

Construction: 

Proof: 

So, by Pythagoras’ theorem, we have

Distinguish between right angle, acute angle and obtuse angle triangle (when sides of the triangle are given)

The Pythagorean Theorem for right triangles states a relationship between the three sides. Let a and b be the lengths of the two sides, and let c be the length of the hypotenuse. Then,

However, if a triangle is not a right triangle, then this equation is not true. There are certain inequalities that will hold for acute and obtuse triangles that are very similar to the Pythagorean Theorem.

Pythagorean Theorem for Acute Triangles

Pythagorean Theorem for Obtuse Triangles

Note that, there is no definitive hypotenuse for a triangle that is acute or obtuse. Therefore we can assign the side lengths of these triangles to the three variable slots in the formula (a, b, and c) in any configuration we wish.