Question

prove that a right angled triangle can never be a regular polygo using two examples.​

Answer 1

Answer:

see below

Step-by-step explanation:

Regular Polygon : a polygon with equal sides

Right Triangle : A polygon with three sides in which a greater side (hypotenuse) must exist.

Ex : 1) no side equal

consider ∆ABC ; ^B = 90° and AB = 3cm & BC = 4cm then by pythogoras theoruem, AC ( hypotenuse) = 5cm

Ex2) two sides equal

consider ∆ABC ; ^B = 90° and AB = 3cm & BC = 3cm then by pythogoras theorem, AC ( hypotenuse) =3√2cm

hence we can never find a right triangle with all sides equal

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other method :

proof by contradiction :

∆ABC ; ^B = 90° and it's a regular polygon

then assume AB = BC = CA = x

By Pythagoras theorem,

AB^2 + BC^2 = AC^2

x^2 + x^2 = x^2

2x^2 = x^2

2 = 1

it's absurd & our assumption is wrong

hence at least one of the sides is different

therefore right triangle is never a regular polygon

hence proved

Answer 2

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