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 \({AB}^{2}=2{AC}^{2}\).

Diagram

 Video Solution
Triangles
Ex 6.5 | Question 4

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

But

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