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

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

In Fig .D is a point on side BC of DeltaABC such that (BD)/(CD) =(AB)/(AC) prove that AD is the bisector of angleBAC.

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

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.

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.

In the figure, ABC is a triangle in which /_C=90^(@) and AB=5cm . D is a point on AB such that AD=3cm and /_ACD=60^(@) . Then the length of AC is

AB is line segment and P is its mid point. D and E are points on the same side of AB such that BAD = ABE and EPA = DPB show that (i) Delta DAP ~= Delta EBP (ii) AD = BE

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