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`.

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 .

If two sides of a triangle are unequal, the longer side has greater angle opposite to it. GIVEN : A A B C in which A C > A Bdot TO PROVE : /_A B C >/_A C B CONSTRUCTION : Mark a point D on A C such that A B=A Ddot Joint B Ddot

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

D is a point on the side BC of a triangle ABC such that /_A D C=/_B A C . Show that C A^2=C B.C D .

A circle touches all the four sides of a quadrilateral A B C D . Prove that: A B+C D=B C+D A .

If D is the mid-point of the side B C of a triangle A B C , prove that vec A B+ vec A C=2 vec A Ddot

In a triangle A B C , if A B=A C\ a n d\ A B is produced to D such that B D=B C , find /_A C D\ :\ /_A D C

In an isosceles triangle altitude from the vertex bisects the base. GIVEN : An isosceles triangle A B C such that A B=A C and an altitude A D from A on side B Cdot TO PROVE : D bisects B C i.e. B D=D Cdot Figure

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 the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base. Given: A triangle A B C in which A B=A C and a circle is drawn by taking A B as diameter which intersects the side B C of triangle at D . To Prove: B D=D C Construction : Join A D .