`A B C` is an isosceles triangle with `A C=B C` . If `A B^2=2\ A C^2` , prove that ` A B C` is right triangle.

ABC is an isosceles triangle with AC = BC. If A B^2=2A C^2 , prove that ABC is a right triangle.

A B C is an isosceles right triangle right-angled at C . Prove that A B^2=2A C^2 .

In a triangle A B C ,\ \ A D_|_B C and A D^2=B DxxC Ddot Prove that A B C is a right triangle.

\ ABC is an isosceles triangle with A B=A C . Side B A is produced to D such that A B=A D . Prove that /_B C D is a right angle.

ABC is an isosceles right triangle, right-angled at C . Prove that: A B^2=2A C^2dot

A B C is an isosceles triangle with A B=A C and D is a point on A C such that B C^2=A CXC D . Prove that B D=B C .

A B C is an isosceles triangle with A B=A C and D is a point on A C such that B C^2=A CxC Ddot Prove that B D=B C

In an isosceles triangle A B C with A B=A C and B D_|_A Cdot Prove that B D^2-C D^2=2C DdotA Ddot

A D and B E are respectively altitudes of an isosceles triangle A B C with A C=B C . Prove that A E=B Ddot

If A B C is an isosceles triangle with A B=A C . Prove that the perpendiculars from the vertices B and C to their opposite sides are equal.