Question

ABC is an isoceles triangle, right angled at C, prove that AB square=2AC square​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

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