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

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

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.

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 .

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 .

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

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

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

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