Question

ABC is an isosceles triangle right angled at C prove that AB square is equal to 2BC square

Answer 1

Answer:

Step-by-step explanation:

Triangle ABC is an isoceles right angled triangle

hence, AC=BC.............(Isoceles triangle's property)......(1)

   ∠ABC=90*.......(given)

   Therefore, in right angled triangle ABC,

  by Pythagoras thm,

  AB² = AC² + BC²

         = BC² + BC²..........(from 1)

  AB² = 2BC²

 hence proved

Answer 2

given:

ABC is the right angle triangle and angle C=90......(1)

also given,

ABCis the isosceles triangle

so AC=BC......(2)

to prove,

${ab}^{2} = 2{bc}^{2}$

proof,

from eq (1)

angleC = 90°

so, by Pythagoras theorem

AB^2=BC^2+AC^2

Now from eq(2)

BC=AC

SO

AB^2=BC^2+BC^2

AB^2=2BC^2

hence proved