`A B C` is a triangle and `D` is the mid-point of `B C` . The perpendiculars from `D` to `A B` and `A C` are equal. Prove that the triangle is isosceles.

A B C is a triangle. D is the mid point of B Cdot If A D is perpendicular to A C , then prove that cos A\ dotcos C=(2(c^2-a^2))/(3a c) .

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 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.

Let A B C be a triangle with A B=A Cdot If D is the midpoint of B C ,E is the foot of the perpendicular drawn from D to A C ,a n dF is the midpoint of D E , then prove that A F is perpendicular to B Edot

The bisectors of the angles B and C of a triangle A B C , meet the opposite sides in D and E respectively. If DE||BC , prove that the triangle is isosceles.

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

In figure, A B C\ a n d\ B D E are two equilateral triangles such that D is the mid-point of B C . If A E intersects B C in F . Prove that: ar(triangle BFE)=2ar(triangle FED) .

In Figure, A B C is a right triangle right angled at B and D is the foot of the the perpendicular drawn from B on A C . If D M_|_B C and D N_|_A B , prove that: (i) D M^2=D NxxM C (ii) D N^2=D MxxA N

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

If A B C is an isosceles triangle and D is a point on B C such that A D_|_B C then,