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`

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

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

If DeltaA B C is an isosceles triangle such that A B=A C ,\ then altitude A D from A on B C bisects B C (Fig.43).

If A B C is isosceles with A B=A C and C(O ,\ r) is the incircle of the A B C touching B C at L , prove that L bisects 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 .

A B C\ a n d\ D B C are two isosceles triangles on the same bas B C and vertices A\ a n d\ D are on the same side of B C . If A D is extended to intersect B C at P , show that A P bisects " "/_A as well as /_D and A P is the perpendicular bisector of B C

A B C is an isosceles triangle in which A B=A C,B E\ a n d\ C F are its two medians. Show that B E=C Fdot

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 D is a parallelogram. A B is produced to E so that B E=A B . Prove that E D bisects B C .