In `Delta ABC, M and N` are points on the sides AB and AC respectively such that `BM=CN`. If `angle A= angle C` then show that `MN||BC`.

In triangle ABC , M and N are points on sides AB and AC respectively. triangle ABN~=triangle ACM , show that triangle AMN~triangle ABC

In Delta ABC, AB = AC. D , E and F are mid-points of the sides BC, CA and AB respectively . Show that : AD and FE bisect each other.

In a right triangle ABC right-angled at B, if P and Q are points on the side AB and AC respectively, then___

In Delta ABC, AB = AC. D , E and F are mid-points of the sides BC, CA and AB respectively . Show that : AD is perpendicular to EF.

In Delta ABC, AB = AC and D is a point an side AC such that AD = BD = BC . Show that : angle ADB = 108 ^(@)

In triangle ABC, angle B is obtuse. D and E are mid-points of sides AB and BC respectively and F is a point on side AC such that EF is parallel to AB. Show that BEFD is a parallelogram.

Let ABC be a triangle. Three points D, E and F are on the sides AB, AC and BC respectively so that BDEF is a parallelogram. M and N are mid points of the sides DE and EF. If vector bar(MN)=(1)/(4)bar(AC) . Then find the ratio in which D and F divides the sides AB and BC.

In the adjoining figure, BM and CN are the altitudes drawn to the sides AC and AB respectively of DeltaABC . If BM=CN, prove that DeltaABC is isosceles.

In the given figure, sides AB and AC of triangle ABC are extended to points P and Q respectively. Also, angle PBC lt angle QCB . Show that AC gt AB