In `DeltaABC`, the bisector AD of A is perpendicular to side BC Show that AB = AC and `DeltaABC` is isosceles.

In DeltaABC , the bisector AD of /_BAC intersects BC at D . Prove that the DeltaABC is an isoceles triangle.

In DeltaABC , AD is the perpendicular bisector of BC (See adjacent figure). Show that DeltaABC is an isosceles triangle in which AB = AC.

In DeltaABC , the bisector of /_ABC intersects AC at the point P . Prove that CB: BA=CP:PA .

In DeltaABC , AB = AC. The perpendiculars drawn from B and C to AC and AB respectively, intersect the sides AC and AB at the points E and F respectively. Prove that FE||BC.

In a DeltaABC , the point D divides BC in the ratio 1:2 Also AD is perpendicular to AB. Then the value of the expression tanB(1+2tanAtanc)-2tanC is:

In a quadrillateral ABCD, it is given that AB ||CD and the diagonals AC and BD are perpendiclar to each other . Show that AD. BC = AB. CD.

AD and BC are equal and perpendiculars to a line segment AB. Show that CD bisects AB.

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

In the adjoining figure AD and BE are the perpendiculars on side BC and CA respectively of the DeltaABC , Then , A, B, D, E are concyclic.

In DeltaABC, D, E and F are the midpoints of sides AB, BC and CA respectively. Show that DeltaABC is divided into four congruent triangles, when the three midpoints are joined to each other. (ΔDEF is called medial triangle)