Ex.6.5 Q4 Triangles Solution - NCERT Maths Class 10

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Question

\(ABC\) is an isosceles triangle right angled at \(C.\) Prove that \(A{{B}^{2}}=\text{ }2A{{C}^{2}}\) .

Diagram

Text Solution

Reasoning:

As we are aware, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Steps:

In \(\,\,\Delta ABC,\,\,\,\,\angle ACB={{90}^{0}}\) and \(AC=BC\)

But

\[\begin{align} A{{B}^{2}}&=A{{C}^{2}}+B{{C}^{2}} \\ & =A{{C}^{2}}+A{{C}^{2}}[\because AC=BC] \\ A{{B}^{2}}&=2A{{C}^{2}} \end{align}\]