In Figure, ` 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`

A D and B E are respectively altitudes of an isosceles triangle A B C with A C=B C . Prove that A E=B Ddot

A D\ a n d\ B E are respectively altitudes of A B C such that A E=B D . Prove that A D=B E .

In an isosceles triangle A B C with A B=A C and B D_|_A Cdot Prove that B D^2-C D^2=2C DdotA Ddot

B D and C E are bisectors of /_B and /_C of an isosceles A B C with A B=A Cdot Prove that B D=C Edot

B D\ a n d\ C E are bisectors of /_B\ a n d\ /_C of an isosceles A B C with A B=A C . Prove that B D=C E

In Figure, D ,E and F are, respectively the mid-points of sides B C ,C A and A B of an equilateral triangle A B C . Prove that D E F is also an equilateral triangle.

In Figure, D ,E and F are, respectively the mid-points of sides B C ,C A and A B of an equilateral triangle A B C . Prove that D E F is also an equilateral triangle.

In Figure, A B=A CdotB E\ a n d\ C F are respectively the bisectors of /_B and /_C . Prove that E C B \ ~=\ F C B

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 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 .