Show that a median of a triangle divides it into two triangles of equal area. GIVEN : A `triangle A B C` in which `A D` is the median. TO PROVE : `a r(triangle A B D)=a r( triangle A D C)` CONSTRUCTION : Draw `A L_|_B C`

Show that a median of a triangle divides it into two triangles of equal areas.

Prove that a median divides a triangle into two triangles of equal area.

A quadrilateral A B C D is such that diagonal B D divides its area in two equal parts. Prove that B D bisects A C GIVEN : A quadrilateral A B C D in which diagonal B D bisects it. i.e. a r( triangle A B D)=a r( triangle B D C) CONSTRUCTION : Join A C Suppose A C and B D intersect at O . Draw A L_|_B D . TO PROVE : A O=O C

A quadrilateral A B C D is such that diagonal B D divides its area in two equal parts. Prove that B D bisects A C . GIVEN : A quadrilateral A B C D in which diagonal B D bisects it. i.e. a r(triangle A B D)=a r(triangle B D C) CONSTRUCTION : Join A C Suppose A C and B D intersect at O . Draw A M_|_B D and C N _|_ B D . TO PROVE : A O=O C .

Show that the diagonals of a parallelogram divide it into four triangles of equal area. GIVEN : A parallelogram A B C D . The diagonals A C and B D intersect at Odot TO PROVE : a r( O A B)=a r( O B C)=a r( O C D)=a r( A O D)

In figure, A B C D is a trapezium in which A B||C D . Prove that: a r( triangle A O D)=a r( triangle B O 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

Prove that the area of an equilateral triangle is equal to (sqrt(3))/4a^2, where a is the side of the triangle. GIVEN : An equilateral triangle A B C such that A B=B C=C A=a . TO PROVE : a r(triangle A B C)=(sqrt(3))/4a^2 . CONSTRUCTION : Draw A D_|_B C .

Prove that any two sides of a triangle are together greater than twice the median drawn to the third side. GIVEN : triangle A B C in which A D is a median. PROVE : A B+A C >2A D CONSTRUCTION : Produce A D to E such that A D=D E . Join E C .

The median of a triangle divides it into two (a)congruent triangle (b) isosceles triangles (c)right triangles (d) triangles of equal areas