A triangle `A B C` is an isosceles triangle if any one of the following conditions hold: Bisector of `/_B A C` is perpendicular to the base `B C`

A triangle A B C is an isosceles triangle if any one of the following conditions hold: Altitude A D bisects /_B A C Bisector of /_B A C is perpendicular to the base B C

A triangle A B C is an isosceles triangle if any one of the following conditions hold: (a) Altitude A D bisects /_B A C (b) Bisector of /_B A C is perpendicular to the base B Cdot

Prove that A B C is isosceles if any one of the following holds: A l t i t u d e\ AD bisects B C Median A D is perpendicular to the base B C

If A B C is an isosceles triangle and D is a point on B C such that A D_|_B C then,

In triangle A B C , base B C and area of triangle are fixed. The locus of the centroid of triangle A B C is a straight line that is a) parallel to side B C (b)right bisector of side BC (c)perpendicular to BC (d)inclined at an angle sin^(-1)((sqrt())/(B C)) to side BC

In Figure, A B C is an isosceles triangle in which A B=A Cdot and C P||A B and A P is the bisector of exterior /_C A D of A B C . Prove that /_P A C=/_B C A and (ii) A B C P is a parallelogram.

A B C is an isosceles triangle. If the coordinates of the base are B(1,3) and C(-2,7) , the coordinates of vertex A

In an isosceles triangle A B C with A B=A C , B D is perpendicular from B to the side A C . Prove that B D^2-C D^2=2\ C D A D

A B C is an isosceles right triangle right-angled at C . Prove that A B^2=2A C^2 .

In any triangle A B C , prove that following: \ \ bcosB+c\ cos\ C="a c o s"(B-C)