Math Revision ch-Geometrical Construction

Extra Questions for Practice 

1. Construct line segments whose lengths are:

(i) 4.8 cm

(ii) 12 cm 5 mm

(iii) 7.6 cm

2. Draw a line PQ. Take a point R on it. Draw a line perpendicular to PQ and passing through R.

(Using (i) ruler and a set-square (ii) ruler and compasses)

3. Draw a line segment of length 8.6 cm. Bisect it and measure the length of each part.

4. Draw an angle of measurement 150 degree. 

Solution: 1

(i) 4.8 cm

Construct a line L on a paper and mark A on it.

Now place the metal point of the compass at zero mark of the ruler.

Make adjustments in the compass such that the pencil point is at 4.8 cm mark on the ruler.

Take compass on L such that its metal point is on A.

Now mark a small mark as B on L which is corresponding to the pencil point of the compass.

Here, AB is the required line segment of length 4.8 cm.

(ii) 12 cm 5 mm

Construct a line L on a paper and mark A on it.

Now place the metal point of the compass at zero mark of the ruler.

Make adjustments in the compass such that the pencil point is at 5 small points from the mark of 12 cm to 13 cm on the ruler.

Take compass on L such that its metal point is on A.

Now mark a small mark as B on L which is corresponding to the pencil point of the compass.

Here, AB is the required line segment of length 12 cm 5 mm.

(iii) 7.6 cm

Construct a line L on a paper and mark A on it.

Now place the metal point of the compass at zero mark of the ruler.

Make adjustments in the compass such that the pencil point is at 6 small points from the mark of 7 cm to 8 cm of the ruler.

Take compass on L such that its metal point is on A.

Now mark a small mark as B on L which is corresponding to the pencil point of the compass.

Here, AB is the required line segment of length 7.6 cm.

Solution: 2

(i) Construct a line PQ and mark a point R on it.

Now place the set square with its one arm of the right angle along the line PQ.

Place the ruler along its edge without disturbing the position of set square.

Remove the set square without disturbing the position of the ruler and construct a line MN through R.

Here, MN is the required line which is perpendicular to PQ through the point R.

(ii) Construct a line PQ and mark R on it.

Considering R as the centre and measuring convenient radius, draw an arc which touches the line PQ at A and B.

Considering A and B as centres and radius which is greater than AR, draw two arcs which cuts each other at the point S.

Now join the points RS and extend in both directions.

Here, RS is the required line which is perpendicular to PQ through the point R.

Solution: 3

Construct a line segment AB of length 8.6 cm.

Taking A as centre and radius which is more than half of line segment AB, construct arcs on both sides of AB.

Taking B as centre and same radius, construct arcs on both sides of AB which cuts the previous arcs at the points E and F.

Construct a line segment from the points E and F which intersects AB at the point C.

By measuring AC and BC we get AC = BC = 4.3 cm.

 Solution: 4

Construct a line AB and mark a point O in the middle of AB.

Taking O as center and convenient radius construct an arc which cuts the line AB at the points P and Q.

Taking Q as center and same radius construct an arc which cuts the previous arc and name it as point R.

Taking R as center and same radius construct an arc which cuts the previous arc and name it as point S.

Taking P and S as centers and radius which is more than half of PS, construct two arcs which cuts each other and name it as point T.

Construct OT and extend it to the point C to form the ray OC.

Here, ∠BOC is the required angle of 150o.