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` .

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

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 quadrilateral A B C D ,\ \ /_B=90o . If A D^2=A B^2+B C^2+C D^2 then prove that /_A C D=90o .

In A B C , /_C is an obtuse angle. A D_|_B C and A B^2=A C^2+3\ B C^2dot Prove that B C=C D .

In Fig. 4.145, if A B_|_B C , D C_|_B C and D E_|_A C , prove that C E D ∼ A B C . (FIGURE)

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 .

In /_\ A B C , given that A B=A C and B D_|_A C . Prove that B C^2=2\ A C * C D

In Figure, if B D_|_A C and C E_|_A B , prove that (i) /_\A E C ~ /_\A D B (ii) (C A)/(A B)=(C E)/(D B)

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 Figure, A B=A C\ a n d\ D B=D Cdot\ Prove that /_A B D=/_A C D