If A, B and C are three points on a line, and B lies between A and C (see figure), then prove that AB + BC = AC.

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

D is a point on side BC ΔABC such that AD = AC (see figure). Show that AB > AD.

E and F are respectively the mid-points of equal sides AB and AC of DeltaABC (see figure) Show that BF = CE.

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see figure) Show that AD = AE

D is a point on side BC of triangle ABC such that AD = AC (see the given figure). Show that AB gt AD.

In right angled DeltaABC, /_C= 90^(@) and D, E, F are three points on BC such that they divide BC in eaual parts (see the given figure). Prove that 8(AF^(2)+AD^(2))= 11AC^(2)+5AB^(2) .

AD and BC are equal perpendiculars to a line segment AB (see the given figure) Show that CD bisects AB.

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 .

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.

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see the given figure). Show that AD = AE.