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

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

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

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.

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. 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.

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

#### SOLUTION

Solution :

Construction of Angles: 1 Mark each

60 angle 30 angle 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 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 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. 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. 