In a triangle ABC, AD is the median drawn on the side BC is produced to E such that `AD = ED` prove that ABEC is a parallelogram.

In triangle ABC, AD is a median. Prove that AB + AC gt 2AD

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

triangle ABC is an isosceles tr ia n g le in w h ich AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that angle BCD is a right angle.

In triangleABC , AD is a median . E is the midpoint of AD and F is the midpoint of AE. Prove that ar(ABF)= 1/8 ar(ABC).

In Delta ABC , AD is a median and E is the midpoint of AD. BE is extended to intersect AC at F. Prove that AF = (1)/(3)AC .

D is a point on the side BC of a triangle ABC such that /_ADC= /_BAC . Show that CA^(2)= CB*CD .

In triangle ABC, AB gt AC and D is any point of BC. Prove that, AB gt AD.

In a triangle ABC , E is the midpoint of median AD. Show that ar(BED) = 1/4 ar(ABC)

ABC is a triangle with AB= AC and D is a point on AC such that BC^(2)= AC xx CD . Prove that BD= BC.

In triangle ABC, AD is the perpendicular bisector of BC (see the given figure). Show that triangle ABC is an isosceles triangle in which AB = AB .