In Figure, `A C > A B\ a n d\ D` is the point on `A C` such that `A B=A Ddot` Prove that `B C > C D`

In Figure, A D=A E\ a n d\ D\ a n d\ E are points on B C such that B D=E Cdot Prove that A B=A 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

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 D is a parallelogram. E is a point on B A such that B E=2\ E A\ a n d\ F is a point on D C such that D F=2\ F Cdot Prove that A E\ C F is a parallelogram whose area is one third of the area of parallelogram A B\ C Ddot

A B C D is a parallelogram. P is a point on A D such that A P=1/3\ A D\ a n d\ Q is a point on B C such that C Q=1/3B C . Prove that A Q C P is a parallelogram.

A ,\ B ,\ C ,\ D are four consecutive points on a circle such that A B=C Ddot Prove that A C=B D

In Figure, A C=A E ,\ A B=A D\ a n d\ /_B A D=/_E A Cdot Prove that B C=D E

In Figure, A B=A C ,\ D is the point in the interior of A B C such that " "/_D B C=" "/_D C Bdot Prove that A D bisects B A C\ of A B Cdot

In Figure, A B C\ a n d\ D B C are two triangles on the same base B C such that A B=A C\ a n d\ D B=D Cdot Prove that /_A B D=/_A C D

In Figure, if A B||D C\ a n d\ P is the mid-point B D , prove that P is also the midpoint of A C