Mathematics
ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2.
Pythagoras Theorem
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Answer
Since, the triangle is right triangle.
Hence, the side opposite to right angle will be hypotenuse and will be the greatest side.
From figure,
Hypotenuse = AB.
The other two sides will be equal as the triangle is also isosceles i.e. (AC = BC)
By pythagoras theorem,
⇒ (AB)2 = (AC)2 + (BC)2
⇒ (AB)2 = (AC)2 + (AC)2
⇒ (AB)2 = 2AC2.
Hence, proved that (AB)2 = 2AC2.
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