Draw a line segment of length 10cm and bisect it. Further bisect one of the equal parts and measure its length.

Steps of construction:

i. Draw a line segment PQ of length 10cm.

ii. With P as centre and radius more than half of PQ, draw two arcs above and below PQ.

iii. With Q as centre and same radius, draw two arcs cutting the arcs drawn in step 2 at E and F respectively.

iv. Draw the line segment EF as end points. Suppose it meets PQ at M.Then M bisects the line segment PQ.

v.  With Q as centre and radius more than half of QM, draw two arcs above and below QM.

vi.  With M as centre and the same radius as in step 5 draw arcs intersecting the previous arcs at R and S.

vii. Draw the line segment with R and S as end points. Suppose it meets QM at A.

viii. Then A bisects QM. AQ = AM = 2.5cm.