Revision Notes on Constructions
Learning Goal
1. The perpendicular bisector of a line segment (using ruler and compass)
2. Perpendicular to a line from a point not on it (using ruler and a compass)
3. The bisector of an angle
Perpendiculars
If two lines intersect in such a way that they make a right angle at the point of intersection then they are perpendicular to each other.
1. The perpendicular bisector of a line segment (using ruler and compass)
Step 1: Draw a line segment AB.
Step 2: Take A as the centre and draw two arcs – one upside and one downside with the radius of more than half of the length of AB. Or you can draw a circle taking A as the centre for the convenience.
Again make the arcs with taking B as the centre so that they intersect the previous arcs.
Step 3: Join the intersections of the arcs and name them as C and D.
Step 4: The required perpendicular bisector of AB is CD. Hence, AO = OB.
2. Perpendicular to a line from a point not on it (using ruler and a compass)
Step 1: P is the point outside the given line l.
Step 2: Take P as the centre and draw a big arc of any radius which intersects line l at two points A and B.
Step 3: Take A and B as radius and draw arcs from both points with the same radius as taken before so that they intersect with each other.
Step 4: Join PQ.
PQ is the perpendicular to line l.
3. The bisector of an angle
An angle bisector is the line segment which divides a particular angle into two equal parts. It is also called the line of symmetry of the angle.
Construction of angle bisector (using a ruler and a compass)
Draw the angle bisector of ∠O.
Step 1: Put the pointer on O and draw an arc of any radius so that it cut the rays at point A and B.
Step 2: Put the pointer on point A and draw an arc of the radius of more than half of AB.
Step 3: While taking B as the centre we will draw an arc of the same radius so that it cut the previous arc at point C.
Step 4: Join OC.OC is the required angle bisector of ∠O.
Hence, ∠BOC = ∠COA.