In Figure, `A B=C Ddot` 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 Cdot`

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 and B D=C Edot Prove that A E B~=A D C

In Fig. 71, if A B C D\ a n d\ C D E F ,\ find \ /_A C E

In Figure, triangle A B C is right-angled at Bdot Give that A B=9C M ,\ A C=15 C M ,\ a n d\ D ,\ E\ are the mid-points of the sides A B\ a n d\ A C respectively, calculate The length of B C (ii) The area of A D E

In Figure, it is given that A B=B C and A D=E C . Prove that A B E~=C B D

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, B E_|_A C ,\ A D is any line from A\ to\ B C intersecting B E in HdotP ,\ Q\ a n d\ R are respectively the mid-points of A H ,\ A B\ a n d\ B Cdot Prove that /_P Q R=90^0

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 Figure, it is given that A B=B C a n d A D=E Cdot Prove that a b e ~= C B D (ii) B D=B E

In Figure, A B C\ a n d\ B D E are two equilateral triangls such that D is the mid-point of B CdotA E intersects B C in Fdot Prove that: a r\ ( B D E)=1/2a r\ ( B A E)