`DeltaABC` is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see figure). Show that `/_BCD` is a right angle.

DeltaABC is an isosceles triangle in which AB = AC. Show that /_ B = /_ C.

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see figure) Show that AD = AE

If Delta ABC is an isosceles triangle with angle C=90^(@) and AC=5 cm, then AB is

If Delta ABC is an isosceles triangle with hat(C ) = 90^(@) and AC = sqrt(8) cm then AB is :

ABC is a right angled triangle in which /_A = 90^@ and AB = AC . Show that /_B = /_C .

ABC is an isosceles triangle right angled at C. Prove that AB^(2) = 2AC^(2) .

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that, (i) AD bisects BC (ii) AD bisects /_ A.

In the figure, ABC is a triangle in which AB= AC. Points D and E are points on the side AB and AC respectively such that AD=AE. Show that points B, C, E and D lie on a same circle.

In the adjacent figure, ABC is a triangle in which angleB = 50^(@) and angleC = 70^(@) . Sides AB and AC are produced. If ‘z’ is the measure of the angle between the bisectors of the exterior angles so formed, then find 'z'.