In a gm ABCD the bisector of angle A also bisect BC at X. Prove tht AD2 AB?
AX bisects angle DAB so angles DAX and XAB are equal. .. .. .. .. .. .. .. .. (i)DA is parallel to CB and AX is an intercept.So angle DAX and AXB are alternate angles and therefore angles DAX and AXB are equal.Therefore, by (i) angles XAB and AXB are equal.Thus triangle BAX is isoscelestherefore AB = BX.BX = 1/2*BC = 1/2*AD (since ABCD is a parallelogram).Therefore AB = BX = AD/2.