In Figure, `a A D\ a n d\ B E` are respectively altitudes of an isosceles triangle `A B C` with `A C=B Cdot` Prove that `A E=B D`

D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD=AE. Prove that B,C,D,E are concylic.

D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD=AE .Prove that B,C,D,E are concylic.

In figure E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If A D_|_B C and E F_|_A C , prove that DeltaA B D ~DeltaE C F .

In Fig. 4.124, E is a point on side C B produced of an isosceles triangle A B C with A B=A C . If A D_|_B C and E F_|_A C , prove that (i) A B D E C F (ii) A BxxE F=A DxxE C . (FIGURE)

D a n d E are, respectively, the points on equal sides A B a n d A C of an isosceles triangle A B C such that B , C , E , a n d D are concyclic as shown in Figure. If O is the point of intersection of C D a n d B E , prove that A O is the bisector of line segment D E

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P\ to\ B C intersects F E\ at Qdot Prove that A Q=Q P

In Figure, A D\ a n d\ B E are medians of A B C\ a n d\ B E||D F . Prove that C F=1/4A C

In Figure, B D and C E are two altitudes of a A B C such that B D=C Edot Prove that A B C is isosceles. Figure

In Figure, it is given that A E=A D and B D=C Edot Prove that A E B~=A D C