In Figure, `A B=C D`. Prove that `B E=D E\ a n d\ A E=C E ,` where `E` is the point of intersecting of `A D\ a n d\ B C`.

D\ a n d\ E are, respectively, the points on equal sides A B\ a n d\ A C of an isosceles triangle A B C such that B ,\ C ,\ E ,\ a n d\ D are concyclic as shown in Figure. If O is the point of intersection of C D\ a n d\ B E , prove that A O is the bisector of line segment D E

In Figure, it is given that A E=A D\ a n d\ B D=C Edot Prove that A E B\ ~= A D C

In Figure, /_E >/_A\ a n d\ /_C >/_D . Prove that A D > E C

In Figure, If A B || C D\ a n d\ C D\ || E F , Find /_A C E .

In Figure, if /_\ A B E~= /_\A C D , prove that /_\ A D E ~ /_\ A B C .

In Figure, A B||C F\ a n d\ B C||E D . Prove that /_A B C=\ /_F D E

In Figure, if A B=A C\ a n d\ B E=C D , prove that A D=A Edot

A B C D is a parallelogram, E\ a n d\ F are the mid-points of A B\ a n d\ C D respectively. G H is any line intersecting A D ,\ E F\ a n d\ B C at G ,\ P\ a n d\ H respectively. Prove that G P=P H

In Figure, A B C D is a parallelogram. E\ a n d\ F are the mid-points of the sides A B\ a n d\ C D respectively. Prove that the line segments A F\ a n d\ C E trisect (divide into three equal parts) the diagonal B D .

In Fig. if A B_|_B C and D E_|_A C . Prove that A B C ~ A E D