In a triangle `A B C ,\ A C > A B` , `D` is the mid-point of `B C` and `A E_|_B C` . Prove that: (i) `A B^2=A D^2-B Cx D E+1/4B C^2`

In figure, ABC is a triangle in which /_A B C=90^@ and A D_|_B C . Prove that A C^2=A B^2+B C^2-2B C.B D .

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

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)=1/4a r\ (\ A B C)

In figure, ABC is triangle in which /_A B C > 90o and A D_|_C B produced. Prove that A C^2=A B^2+B C^2+2B C.B D .

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)

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 F E)=\ 2\ a r\ (E F D)

D is the mid-point of side B C of \ A B C\ a n d\ E is the mid-point of B Ddot If O is the mid-point of A E , prove that a r\ (\ B O E)=1/8a r\ (\ A B C)

Let A B C be an isosceles triangle with A B=A C and let D ,\ E ,\ F be the mid points of B C ,\ C A\ a n d\ A B respectively. Show that A D_|_F E\ a n d\ A D is bisected by F E

In Figure, ABD is a triangle right-angled at A and A C_|_B D . Show that (i) A B^2=B C.B D (ii) A C^2=B C.D C (iii) A D^2=B D.C D

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot GIVEN : A A B C ,D is the mid-point of B C and E is the mid-point of the median A Ddot TO PROVE : a r( B E D)=1/4a r( A B C)dot