Question

ABC is an isosceles right triangle, right angled at C. Prove that AB2 = 2AC2

Answer 1

Given data :

Δ ABC is a right Δ and also isosceles triangle.,  

To prove:

$\mathrm{AB}^{2}=2 \mathrm{AC}^{2}$

Step 1:

Proof:

Here,  

Hypotenuse = AB

Also, as it is given that, ΔABC is isosceles,  

Step 2:

AC = BC   [equal sides of isosceles Δ]  

Using Pythagoras theorem,  

Step 3:

In Δ ABC, we have ;

$\begin{array}{l}{\mathrm{AB}^{2}=\mathrm{AC}^{2}+\mathrm{BC}^{2}} \\ {\mathrm{AB}^{2}=\mathrm{AC}^{2}+\mathrm{AC}^{2}}\end{array}$ [AC = BC]  

\mathrm{AB}^{2}=2 \mathrm{AC}^{2}

Hence proved

Answer 2

Answer:

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