line segment pq take a point m and verify pm=mq

Draw a line segment pq of any length then put the pointer of the compass on p and open the compass more than the half of pq like this

then draw arcs on both side of the line segment like this

then without harming the radius of the compass move the pointer to q and repeat the previous step like this

then label the point of intersection of both arcs on both sides as r and s and then join the r and s point with a line . the point where the line will meet on the line segment label it as m like this

we conclude that pm=pq