Construct an angle ∠BAC = 90° on a line segment AB = 6 cm. Cut AC = 5 cm. Bisect AC at D. Measure AD and DC.

Steps of Construction

1. Draw a line segment AB = 6 cm.
2. Taking A as centre and some radius, draw an arc of a circle, which intersects AB, say at a point P.
3. Taking P as centre and with the same radius as before, draw an arc intersecting the previously drawn arc, say at a point Q.
4. Taking Q as centre and with the same radius as before, drawn an arc intersecting the arc drawn in step 1, say at R.
5. Next, taking Q and R as centres and with the radius more than QR, draw arcs to intersect each other, say at S.
6. Draw the ray AS.
7. From ray AS, cut off AC = 5 cm.

Then. ∠BAC = 90° is such that AB = 6 cm and AC = 5 cm.
8. Taking A and C as centres and radius more than  AC. draw arcs on both sides of the line segment AC (to intersect each other).

9. Let these arcs intersect each other at M and N. Join MN.
10. Let MN intersect AC at the point D.
Then, AD = DC
By measurement,
AD = DC = 2.5 cm