Question

ABC is an isosceles triangle with AC= BC if AB square = 2 AC square, prove that triangle ABC is an right angle triangle

Answer 1

given:triangle ABC is an isosceles triangle with
AC=BC
to prove: triangle ABC is an right angle triangle
proof:
$ab { }^{2} = 2ac {}^{2}$
it follows the Pythagoras theorem:
hypotenuse square = base square +height square
$ab {}^{2} = ac {}^{2} + bc {}^{2}$
$ab {}^{2} = ac {}^{2} + ac {}^{2} (ac = bc)$
$ab {}^{2} = 2ac {}^{2}$

since it follows the Pythagoras theorem it is proved that it is a right angled Triangle