Question

Converse of pythagoras theorem

Answer 1

Pythagorean Theorem Converse: A triangle is said to be a right-angled theorem, if the square of one side of a triangle is equal to the sum of the squares of the other two sides.

For eg: If we take triangle ABC 
So if c^2 = a^2 + b^2 holds
then triangle ABC is a right angled triangle with right angle at C.

Answer 2

$\bf\huge\mathfrak{Answer}$

Statement:

In a Triangle the square of longer side is equal to the sum of squares of the other two sides, then the triangle is a right angled triangle.

Given -

A Triangle ABC such that

BC² = AB² + AC²

To Prove -

Angle A = 90°

Construction -

Draw a ∆DEF such that AB = DE and AC = DF and Angle D = 90°

Proof -

In ∆ABC,

BC² = AB² + AC² - Given

In ∆ DEF

EF² = DE² + DF²

Therefore,

EF² = AB² + AC²

(Since AB = DE, AC = DF)

Therefore,

BC² = EF² ie - BC = EF

Now, In ∆ABC and ∆DEF

AB = DE - By Construction

AC = DF - By Construction

BC = EF

Therefore

∆ABC ≅ ∆DEF by SSS test.

Thus,

Angle A = Angle D - CPCT

But, Angle D = 90° ( As per construction)

Therefore

Angle A = 90°

Hence Proved!