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 C* D E+1/4B C^2`

In right-angled triangle A B C in which /_C=90^@ , if D is the mid-point of B C , prove that A B^2=4\ A D^2-3\ A C^2 .

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

A B C is a triangle in which A B=A C and D is any point in B C . Prove that A B^2-A D^2=B D C D .

In a right A B C right-angled at C , if D is the mid-point of B C , prove that B C^2=4\ (A D^2-A C^2) .

In an isosceles triangle A B C with A B=A C , B D is perpendicular from B to the side A C . Prove that B D^2-C D^2=2\ C D A D

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 is a triangle in which D is the mid-point of B C and E is the mid-point of A D . Prove that area of B E D = 1/4 area of ABC.

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

A B C is an isosceles triangle in which A B=A C . If D\ a n d\ E are the mid-points of A B\ a n d\ A C respectively, Prove that the points B ,\ C ,\ D\ a n d\ E are concyclic.

If D is the mid-point of the hypotenuse A C of a right triangle A B C , prove that B D=1/2A C