Question

Using ruler and compasses only, draw a right angle.

Answer 1

We can construct a 90º angle either by bisecting a straight angle or using the following steps.

Step 1:  Draw the arm PA.
Step 2:  Place the point of the compass at Pand draw an arc that cuts the arm at Q.
Step 3:  Place the point of the compass at Qand draw an arc of radius PQ that cuts the arc drawn in Step 2 at R.
Step 4:  With the point of the compass at R, draw an arc of radius PQ to cut the arc drawn in Step 2 at S.
Step 5:  With the point of the compass still at R, draw another arc of radius PQ near Tas shown.
Step 6:  With the point of the compass at S, draw an arc of radius PQ to cut the arc drawn in step 5 at T.
Step 7:  Join T to P. The angle APT is 90º.