Let be a line segment and let C be the midpoint of . Extend to D such that B lies between A and D. Prove that AD + BD = 2CD.

What is the angle between the hour’s hand and minute’s hand of a clock at (i) 1.40 hours, (ii) 2.15 hours? (Use 1° = 60 minutes.)

How much would hour’s hand have moved from its position at 12 noon when the time is 4.24 p.m.?

Let and be two lines intersecting at a point O. Let be a ray bisecting ∠BOD. Prove that the extension of to the left of O bisects ∠AOC.

Let be a ray and let and be two rays on the same side of , with between and . Let be the bisector of ∠AOB. Prove that

∠XOA + ∠XOB = 2∠XOC