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

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.

In /_\ A B C , if A D_|_B C and A D^2=B DxxD C , prove that /_B A C=90dot .

In Figure, if A D_|_B C and (B D)/(D A)=(D A)/(D C) , prove that A B C is a right triangle.

In A B C , if B D_|_A C and B C^2=2\ A C C D , then prove that A B=A C .

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.

In Figure, A D_|_B C and B D=1/3C Ddot Prove that 2C A^2=2A B^2+B C^2

\ 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.

A D ,\ B E\ a n d\ C F , the altitudes of A B C are equal. Prove that A B C is an equilateral triangle.

A D ,\ B E\ a n d\ C F , the altitudes of A B C are equal. Prove that A B C is an equilateral triangle.