In Figure, `A D` is a median and `B L ,\ C M` are perpendiculars drawn from `B\ a n d\ C` respectively on `A D\ a n d\ A D` produced. Prove that `B L=C M`

In Figure, A D is the median and D E||A B . Prove that B E is the median.

In a A B C ,\ B M\ a n d\ C N are perpendiculars from B\ a n d\ C respectively on any line passing through Adot If L is the mid-point of B C , prove that M L=N L .

In Figure, A D\ a n d\ B E are medians of A B C\ a n d\ B E||D F . Prove that C F=1/4A C

B D is one of the diagonals of a quadrilateral A B C Ddot\ \ A M\ a n d\ C N are the perpendiculars from A\ a n d\ C , respectively, on B Ddot Show That a r\ (q u a ddotA B C D)=1/2B Ddot(A M+C N)

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L C M)=a r\ ( L B M)

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L B C)=\ a r\ (\ M B C)

In a A B C , If L a n d M are points on A B a n d A C respectively such that L M B Cdot Prove that: a r ( A B M)=a r ( A C L)

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L O B)=a r\ (\ M O C)

In Figure, B M a n d D N are both perpendiculars to the segments A C a n d B M=D N . Prove that A C bisects B D

In Figure, X\ a n d\ Y are the mid-points of A C\ a n d\ A B respectively, Q P\ B C\ a n d\ C Y Q\ a n d\ B X P are straight lines. Prove that a r\ (\ A B P)=\ a r\ (\ A C Q)