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

In the adjacent figure the sides AB and AC of Delta ABC are produced to points E and D respectively. If bisectors BO and CO of angleCBE and angleBCD respectively meet at point O, then prove that angleBOC = 90^(@)-(1)/(2) angleBAC .

In the given figure, if AC = BD, then prove that AB = CD.

In triangle ABC, AC gt AB . AB is extended to P and AC is extended to Q. Prove that, angle PBC lt angle QCB .

In the adjacent figure, we have AC = XD, C and D are mid points of AB and XY respectively. Show that AB = XY.

In the given figure, angle B lt angle A and angle C lt angle D . Show that AD lt BC.

In the given figure, AC = AE, AB = AD and angle BAD = angle EAC . Show that BC = DE.

If in a triangle AB=a,AC=b and D,E are the mid-points of AB and AC respectively, then DE is equal to

In the given figure, A, B and C are points on OP, OQ and OR respectively such that AB||PQ" and "AC||PR . Show that BC||QR .

If a line intersects sides AB and AC of a triangleABC at D and E respectively and is parallel to BC, prove that (AD)/(AB)=(AE)/(AC) (see the given figure).

In the adjacent figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC||PR. Show that BC || QR.