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

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

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 .

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.

Fill in the blanks in the following so that each of the following statements is true. (i) Sides opposite to equal angles of a triangle are ....... (ii) Angle opposite to equal sides of a triangle are ....... (iii) In an equilateral triangle all angles are ....... (iv) In a A B C if /_A=/_C , then A B=\ ..... (v) If altitudes C E\ a n d\ B F of a triangle A B C are equal, then A B= ........ (vi) In an isosceles triangle A B C with A B=A C , if B D\ a n d\ C E are its altitudes, then B D is .......... C E . (vii) In right triangles A B C\ a n d\ D E F , if hypotenuse A B=E F and side A C=D E , then A B C\ ~= ....

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 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 .

In Figure, X ,\ Y\ are two points on equal sides A B\ a n d\ A C of a A B C such that A X=A Ydot Prove that X C=Y B