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

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

A diagonal of a parallelogram divides it into two triangles of equal area. GIVEN : A parallelogram A B C D in which B D is one of the diagonals. TO PROVE : ar ( A B D)=a r( C D B)

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)

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)

Prove that any two sides of a triangle are together greater than twice the median drawn to the third side. GIVEN : 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 Edot Join E Cdot

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 .

Prove that the perimeter of a triangle is greater than the sum of the three medians. GIVEN : A A B C in which A D ,B E and C F are its medians. TO PROVE : A B+B C+A C > A D+B E+C F

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 Cdot GIVEN : A quadrilateral A B C D in which diagonal B D bisects it. i.e. a r( A B D)=a r( B D C) CONSTRUCTION : Join A C Suppose A C and B D intersect at O . Draw A L_|_B D and C M B Ddot TO PROVE : A O=O Cdot

Angles opposite to two equal sides of a triangle are equal. GIVEN : A B C in which A B=A C TO PROVE : /_C=/_B CONSTRUCTION : Draw the bisector A D of /_A which meets B C in D Figure

Angles opposite to two equal sides of a triangle are equal. GIVEN : A B C in which A B=A C TO PROVE : /_C=/_B CONSTRUCTION : Draw the bisector A D of /_A which meets B C in D Figure