True or False: If in triangle ABC, (AB)^2 + (BC)^2 = (AC)^2, then triangle ABC is a right triangle

Question

It is a true or false question

Answer 1

This is true only if Angle at B is right angle

Not true in general 

Answer 2

True, because the Pythagorean Theorem is one of those theorems whose converse is also (proven) true.

Answer 3

Yes, that is true for any triangle. That means if you have above given relation (e.g. Pythagorean theorem) for any arbitrary triangle than this triangle is right triangle.

 

One proof of this can be deducted from The Law of Cosines (also called the Cosine Rule).

       

Answer 4

This is the use of Pythagorean theorem.  We can use this theorem if we have a right triangle.

 

AB and BC are the two legs.  AC is the hypotenuse.

 

 

True.

Answer 5

Given:  (AB)² + (BC)² = (AC)²

 

Let θ = angle between sides AB and BC.

 

Then from the law of cosines, true for any plane triangle,

 

(AB)² + (BC)² - 2(AB)(BC)cosθ = (AC)²

 

But since (AB)² + (BC)² = (AC)²,

 

(AC)² - 2(AB)(BC)cosθ = (AC)²

 

⇒ 2(AB)(BC)cosθ = 0

 

AB ≠ 0, BC ≠ 0, so cosθ = 0 ⇒ θ =90° ⇒ right triangle