question_answer 6)

If B is the mid-point of \[\overline{AC}\] and C is the mid-point of \[\overline{BD}\], where A, B, C and D lie on a straight line, say why AB = CD ?

Answer:

Given, B is the mid-point of \[\overline{AC}\]. AB = BC ...(i) and C is the mid-point of \[\overline{BD}\]. \[\therefore \] BC = CD ...(ii) i.e. Now, on adding Esq. (i) and (ii), we get AB + BC = BC + CD AB = CD Hence proved.