ABC is an isosceles triangle with AC = BC. If AB² = 2AC², Prove that ABC is a right triangle.
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ABC is an isosceles triangle with AC = BC. If AB² = 2AC², Prove that ABC is a right triangle.
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Answer:
We know that, 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 the first side is a right angle.
ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.
In ΔABC,
It is given that AC = BC and AB2 = 2 AC2
⇒ AB2 = AC2 + AC2
⇒ AB2 = AC2 + BC2 [Since AC = BC]
As the above equation satisfies Pythagoras theorem, we can say that
⇒ ∠ACB = 90°
Therefore, ΔABC is a right triangle