D is a point on side BC ΔABC such that AD = AC (see figure). Show that AB > AD.

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.

Delta ABC is an equilateral triangle . D is a point on the side BC such that BD = (1)/(3) BC . Prove that 7 AB^(2) = 9AD^(2)

In an equilateral triangle ABC, D is a point on side BC such that BD = (1)/(3) BC. Prove that 9 AD^(2) = 7 AB^(2) .

E and F are respectively the mid-points of equal sides AB and AC of DeltaABC (see figure) Show that BF = CE.

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

ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure) . Show that (i) DeltaABD ~= DeltaACE (ii) AB = AC i.e., ABC is an isosceles triangle.

AB and CD are respectively the smallest and longest sides of aquadrilateral ABCD (see adjacent figure). Show that /_A > /_C and /_ B > /_ D.

E is the mid point of side OB of triangle OAB . D is a point on AB such that AD : DB = 2 : 1 . If OD and AE intersect at P , then -

In the figure, ΔABC, D, E, F are the midpoints of sides BC, CA and AB respectively. Show that (i) BDEF is a parallelogram (ii) ar(DeltaDEF)=1/4ar(DeltaABC) (iii) ar(BDEF)=1/2ar(DeltaABC)

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