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

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

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

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

Diagonal AC of a parallelogram ABCD bisects angleA . Show that (i) it bisects angleC alo (ii) ABCD is a rhombus.

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

In the given Figure AB and CD are intersecting at ‘O’, OA = OB and OD = OC. Show that (i) Delta AOD ~= DeltaBOC and (ii) AD || BC .

D is the midpoint of the side BC of Delta ABC . If P and Q are points o AB and on AC such that DP bisects angle BDA and DQ bisects angle ADC , then prove that PQ || BC

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

BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

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.