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Question

ABC is an isosceles triangle with AC=BC. If AB2=2AC2 prove that ABC is a right triangle.


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Solution

Proving that ABC is a right angle triangle :

Given:

ABC is an isosceles triangle

AC=BC

and

AB2=2AC2

To prove:

ABC is a right triangle.

Or

AC2+BC2=AB2

Proof:

In ΔACB,

AC=BC

The angles corresponding to these sides are equal so these two angles must be less than 90 degrees.

From the given,

AB2=2AC2AB2=AC2+AC2

AB2=AC2+BC2[Since,AC=BC]

By the Pythagoras theorem,ΔABC is a right-angle triangle.

Hence we proved thatΔABC is a right-angle triangle.


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