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`

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 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

If the bisector of the vertical angle of a triangle bisects the base of the triangle. then the triangle is isosceles. GIVEN : A A B C in which A D is the bisector of /_A meeting B C in D such that B D=D Cdot TO PROVE : A B C is an isosceles triangle.

Show that the difference of any two sides of a triangle is less than the third side. GIVEN : A A B C TO PROVE : (i) A C-A B

The sum of any two sides of a triangle is greater than the third side. GIVE : A 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 Ddot

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 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=adot TO PROVE : a r( A B C)=(sqrt(3))/4a^2 CONSTRUCTION : Draw A D_|_B Cdot

In a right angled triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side. GIVEN : A A B C in which /_B=90^0 and /_A C B=2/_C A B . to prove : A C=2B C CONSTRUCTION : Produce C B to D such that B D=C Bdot Join A Ddot