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 .

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

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

Parallelogram A B C D and rectangle A B E F have the same base A B and also have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle. GIVEN : A ||^(gm)A B C D and a rectangle A B E F with the same base A B and equal areas. TO PROVE : Perimeter of ||^(gm)A B C D > Perimeter of rectangle ABEF i.e. A B+B C+C D+A D > A B+B E+E F+A F

Parallelogram A B C D and rectangle A B E F have the same base A B and also have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle. GIVE : A ^(gm)A B C D and a rectangle A B E F with the same base A B and equal areas. TO PROVE : Perimeter of ^(gm)A B C D > P e r i m e t e rofr e c t a nge l ABEF i.e. A B+B C+C D+A D > A B+B E+E F+A F

Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle. GIVE : Two s A B C and D E F such that /_B=/_E ,/_C=/_F and B C=E F TO PROVE : A B C~=D E F

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

The sum of any two sides of a triangle is greater than the third side. GIVE : A triangle A B C TO PROVE : A B+A C > B C ,A B+B C > A C and B C+A C > A B CONSTRUCTION : Produce side B A to D such that A D=A Cdot Join C D .