Question

ABC is an isosceles triangle right angled at C.

Prove that, AB2 = 2AC2.

Answer 1

Step-by-step explanation:

Given data :

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

To prove:

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

2

=2AC

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{gathered}\begin{array}{l}{\mathrm{AB}^{2}=\mathrm{AC}^{2}+\mathrm{BC}^{2}} \\ {\mathrm{AB}^{2}=\mathrm{AC}^{2}+\mathrm{AC}^{2}}\end{array}\end{gathered}

AB 2 =AC 2 +BC 2 AB 2 =AC 2 +AC 2

[AC = BC]

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

Hence proved