Question 4
ABC is an isosceles triangle right angled at C. Prove that $A B^{2} = 2 A C^{2}$ .

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Solution

Given that $Δ A B C$ is an isosceles triangle right angled at C.
In $Δ A C B$ ,
$∠ C = 90^{\circ}$
AC = BC (Given)
$\Rightarrow$ $A B^{2} = A C^{2} + B C^{2}$ ([By using Pythagoras theorem]
$\Rightarrow$ $A B^{2} = A C^{2} + A C^{2}$ [Since, AC = BC]
$\Rightarrow$ $A B^{2} = 2 A C^{2}$

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