Prove that the perimeter of a triangle is greater than the sum of its three medians. Given : A ` A B C` in which `A D ,\ B E\ a n d\ C F` are its medians. To Prove: `A B+B C+A C > A D+B E+C F`

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

Show that the sum of the three altitudes of a triangle is less than the sum of three sides of the triangle. GIVEN : A A B C in which A D_|_B C ,B E_|_A C and C F_|_A Bdot PROVE : A D+B E+C F

Show that the sum of the three altitudes of a triangle is less than the sum of three sides of the triangle. GIVEN :triangle A B C in which A D_|_B C ,B E_|_A C and C F_|_A Bdot PROVE : A D+B E+C F < A B+B C+A 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 .

A B C is an isosceles triangle in which A B=A C,B E\ a n d\ C F are its two medians. Show that B E=C Fdot

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

In Figure, A B C D ,\ A B F E\ a n d\ C D E F are parallelograms. Prove that a r( A D E)=a r( B C F)

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

In Figure, A B C D ,\ A B F E\ a n d\ C D E F are parallelograms. Prove that a r( /_\A D E)=a r( /_\B C F)

In an equilateral triangle, prove that the centroid and centre of the circum-circle (circum centre) coincide) Given : An equilateral triangle A B C in which D , E a n d F are the mid-points of sides B C , C A a n d A B respectively. To Prove: The centroid and circum centre are coincident. Construction : Draw medians A D , B E a n d C F