# Free Practical Geometry Subjective Test 01 Practice Test - 6th grade

### Question 1

Name four tools used for drawing shapes. [1 MARK]

#### SOLUTION

Solution :The four tools used for drawing shapes are:

i) Rulers

ii) Compasses

iii) Set squares

iv) Protractor

### Question 2

Construct a circle of radius 10 cm. What is the diameter of the circle? [2 MARKS]

#### SOLUTION

Solution :Construction: 1 Mark

Diameter: 1 Mark

The circle can be drawn using a ruler and compass.

The diameter of the circle

=2× radius =2×10=20cm

### Question 3

Construct a line segment AB of length 4.2 cm using a compass and a ruler. How many lines can be drawn from the point A? [2 MARKS]

#### SOLUTION

Solution :Construction: 1 Mark

Solution: 1 Mark

The figure shows a line segment AB.

From a single point, an infinite number of lines can be drawn.

∴ From point A, infinite lines can be drawn.

### Question 4

Construct a line segment AB of length 5.6 cm using a compass and ruler. Write the steps. [3 MARKS]

#### SOLUTION

Solution :Each steps: 1 Mark

Step 1: Draw a line l. Mark a point A on the line.

Step 2: Place the compass pointer on the zero mark of the ruler. Open it to place the pencil point up to the 5.6 cm mark.

Step 3: Taking caution that the opening of the compass has not changed the measured length, place the pointer on A and swing an arc to cut l at B.

Step 4: AB is a line segment of the required length.

### Question 5

AB is a line segment. Construct PQ if PQ is twice the length of AB. [3 MARKS]

#### SOLUTION

Solution :Constructing PQ: 1 Mark

Steps: 2 Mark

Steps for constructing PQ based on the length of AB:

(i) Let AB be the line segment.

(ii) Adjust the compass up to the length of AB.

(iii) Draw any line l and mark a point P on it.

(iv) Put the pointer on P and without changing the setting of the compass, draw an arc to cut the line segment at point X.

(v) Now, put the pointer on X and again draw an arc with the same radius as before, to cut the line l at the point Q.

PQ is the required line segment.

### Question 6

Construct 60∘ , 45∘ and 30∘ with ruler and compass. [3 MARKS]

#### SOLUTION

Solution :Construction of Angles: 1 Mark each

60∘ angle

30∘ angle

### Question 7

AB is a line of length 6 cm. Construct a line perpendicular to AB. [4 MARKS]

#### SOLUTION

Solution :Each step: 1 Mark

Step 1: Draw a line of length 6 cm. Mark a point P on it.Step 2: With P as the centre and a convenient radius, construct an arc intersecting the line l at two points A and B.

Step 3: With A and B as centres and a radius 3 cm, construct two arcs, which cut each other at Q.

Step 4: Join PQ. Then PQ is perpendicular to l

### Question 8

Draw an angle of 132∘ and construct its bisector. [4 MARKS]

#### SOLUTION

Solution :Each step: 1 Mark

The steps given below should be followed to construct an angle and its bisector:

i) Draw a line l and mark a point 'O' on it.

ii) Mark a point A 132∘ to line l with the help of protractor. Join OA.

iii) Draw an arc of convenient radius, while taking point O as the centre. Let it intersect both rays of angle 132∘ at point A and B.

iv) Taking A and B as centres, draw arcs each of radius more than half of AB so that they intersect each other at C. Join OC.

OC is the required bisector of angle of 132∘

### Question 9

Draw AB of length 6.8 cm and find its axis of symmetry. [4 MARKS]

#### SOLUTION

Solution :Each step: 1 Mark

(i) Draw a line segment AB of length 6.8 cm.

(ii) Taking A as the centre, draw a circle by using a compass. The radius of the circle should be more than half of AB.

(iii) With the same radius as before, draw two arcs using B as the centre such that it cuts the previous circle at C and D.

(iv) Join CD. CD is the axis of symmetry.

### Question 10

Draw a line 8.4 cm and divide it into four parts using a compass. [4 MARKS]

#### SOLUTION

Solution :Steps: 2 Marks

Construction: 2 Marks

i) Draw a line segment XY of length 8.4 cm.

ii) Draw a circle, while taking point X as centre and radius more than half of XY.

iii) With same radius and taking the centre as Y, again draw arcs to cut the circle at A and B. Join AB which intersects XY at M.

iv) Taking X and Y as centres. Draw two circles more than half of XM.

v) With same radius and taking M as the centre, draw arcs to intersect these circles at P, Q, R and S.

vi) Join PQ and RS. These are intersecting XY at T and U.

vii) Now XT = TM = MU = UY. These are 4 equal parts of XY.