ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 13 Practical Geometry Check Your Progress

Question 1.
Draw a line segment AB = 5.4 cm. Construct a perpendicular at A by using ruler and compass.
Solution:
Steps of construction:

1. Draw AB = 5.4 cm.
2. With any radius draw an arc which cuts AB at M.
3. With M as centre and the same radius
cut the previous arc at N and P.
4. With N and P as centres draw arcs which intersect at L.
Join AL.
5. AL is required perpendicular.

Question 2.
Draw a line segment PQ = 6.8 cm. Draw a perpendicular to it from a point A outside PQ by using ruler and compass.
Solution:

Steps of construction:

1. Draw a line segment PQ = 6.8 cm
and take a point A outside PQ.
2. With A as centre and any suitable radius,
draw an arc to cut line PQ at point C and D.
3. With C and D as centres,
draw two arcs of equal radius cutting each other
at B on the other side of line PQ.
4. Join AB to meet the line PQ at M.

Question 3.
Draw a line segment of length 6.5 cm and construct its axis of symmetry.
Solution:
Steps of construction:

1. Draw a line segment $$\overline{\mathrm{AB}}$$ of length 6.5 cm.
2. With A as centre, using a compass, draw a circle.
The radius of this circle should be more than half of the length of $$\overline{\mathrm{AB}}$$.
3. With the same radius and with B as centre,
draw another circle using a compass.
Let it cut the previous circle at C and D.
4. Join CD. Then, $$\overline{\mathrm{CD}}$$ is the axis of symmetry of $$\overline{\mathrm{AB}}$$.

Question 4.
Draw ∠AOB = 76° with help of a protractor. Bisect this angle by using ruler and compass. Measure the two parts by your protractor and see how accurate you are.
Solution:
Steps of construction:

1. Draw a line segment OB.
2. Construct ∠AOB with the help of protector = 76°.
3. With the help of compass and O as centre
draw an arc meeting OB and OA at P and Q respectively.
4. With P and Q as centre and radius more than $$\frac{1}{2}$$ PQ
draw two arcs meeting each other at R.
5. OD is the bisector of ∠AOB.
6. On measuring ∠AOD = ∠DOB = 38°.

Question 5.
By using and compass, construct an angle of 135° and bisect it. Measure any one part by protractor and see how accurate you are.
Solution:
Steps of construction:

1. Draw a line OB with help of ruler.
2. With O as a centre and any suitable radius
draw an arc to meet OB at S.
3. With S as a centre and same radius
draw an arc to meet the previous arc at L.
With L as centre and same radius draw another arc M.
Again M as centre draws another arc to meet the first arc at N.
4. With M and N as centres draw two arcs of
equal radius $$\left(>\frac{1}{2} \mathrm{SL}\right)$$ cutting each other at A.
5. Join OA intersecting the radius at point Q.
6. Now taking Q and M as a centres
draw two arcs of equal radius cutting each other at P.
7. Join PO.
8. Measuring the ∠POB with protractor we get ∠POB equal to 135°.
9. Taking S and R as a centres draw two arcs cutting each other at T.
Join TO.
10. ∠TOB is the bisector of ∠POB. ∠TOB = ∠TOP = 67.5°.