# Free Practical Geometry Subjective Test 02 Practice Test - 6th grade

Draw a circle and mark a point X on the exterior of the circle and point Y in the interior of the circle. [1 MARK]

#### SOLUTION

Solution : Define line segment and construct a line segment AB of length 3.9 cm using compass and ruler. [2 MARKS]

#### SOLUTION

Solution :

Definition: 1 Mark
Construction: 1 Mark

A line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. With the point O as the centre, draw two circles of radius 2.5 cm and 4 cm with compass and ruler. What are these circles called? [2 MARKS]

#### SOLUTION

Solution :

Construction: 1 Mark

Steps of construction:

1. Stretch the compass to the length of 2.5 cm measuring with a ruler. Then draw a circle with the centre as O.
2. Again stretch the compass to the length of 4 cm measuring with a ruler. Then draw a circle with the same centre O as shown below. These are known as concentric circles as they have the same centre but different radius.

Draw an angle of 90 and construct its bisector. [3 MARKS]

#### SOLUTION

Solution :

Construction of angle: 1 Mark
Construction of bisector: 1 Mark
Steps: 1 Mark

Steps of construction:
i) Make a right-angled triangle using a compass.
ii) With R and V as centre make arcs at any point in the mid of the angle.
iii) That point W will be the required point.
iv) Join P and W. PW is the required bisector. Draw a circle of radius 4 cm. Draw two lines touching the circumference of the circle such that they intersect at an angle 60⁰. Draw a quadrilateral joining the centre of circle, points at which lines are touching and at the point they intersect. [3 MARKS]

#### SOLUTION

Solution :

Construction of circle: 1 Mark
Construction of intersecting lines: 1 Mark

Construction:

1) Draw a circle of radius 4 cm with centre O.

2) Take a point A on the circle. Join OA.

3) Draw a perpendicular to OA at A.

4) Draw a radius OB, making an angle of 120° (180° – 60°) with OA.

5) Draw a perpendicular to OB at point B. Let these perpendiculars intersect at P.

6) PA and PB are the required tangents inclined at angle of 60° Draw a circle with centre O using compass and ruler. Make smaller circles such that they are:
i) non-intersecting
ii) passing through the point O
iii) touching the circumference of the bigger circle. [3 MARKS]

#### SOLUTION

Solution :

Construction: 2 Marks
Steps: 1 Mark

Steps of construction:
i) Draw a circle of any radius.
ii) Draw a smaller circle of radius half of the radius of the larger circle and at the midpoint of the radius in one direction.
iii) In the same way, draw the smaller circle in the opposite direction. On a circle of radius 3 cm draw its two chords. Then construct the perpendicular bisector of these chords. Where do they meet? [4 MARKS]

#### SOLUTION

Solution :

Construction of circle: 1 Mark
Construction of chords: 1 Mark
Construction of bisector: 1 Mark
Meeting point: 1 Mark

i) Mark any point C on the sheet. Now, by adjusting the compass up to 3 cm and by putting the pointer of compass, draw the circle. It is the required circle of 3 cm radius.

ii) Take any two chords AB and CD in the circle.

iii) Taking A and B as centres and with radius more than half of AB, draw arcs on both sides of AB, intersecting each other at E, F. Join EF which is the perpendicular bisector of AB.

iv) Taking C and D as centres and with radius more than half of CD, draw arcs on both sides of CD, intersecting each other at G and H . Join GH which is the perpendicular bisector of CD.

Now, we find that EF and GH meet at the centre of circle O. Draw an angle 135 and divide it into four parts. [4 MARKS]

#### SOLUTION

Solution :

Construction of angle: 1 Mark
Division into 4 parts: 2 Marks
Steps: 1 Mark

i) Make an angle 135 using a protractor.
ii) With the centre as O. Draw a small arc AB.
iii) With A and B as centre draw arcs of radius more than half of AB at C.
iv) In the same way, draw arcs taking the centre as B and D at F and with centres at A and D at E.
v) Join OE, OC, OF. (a) Draw an angle 115 and construct its bisector. [2 MARKS]
(b)
Suppose an angle (whose measure we do not know) is given and you have to make a copy of this angle. How will you do it? [2 MARKS]

#### SOLUTION

Solution :

(a) 2 Marks
(b) 2 Marks

(a) 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 at 115 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 the 115 angle at point A and B.
iv) Taking A and B as centres, draw an arc of radius more than 12  AB in the interior of the angle of 115. Let those intersect each other at C. Join OC.

OC is the required bisector of the angle of 115 (b)
As usual, we will have to use only a straight edge and the compass.

Given A, whose measure is not known. Step 1: Draw a line l and choose a point P on it. Step 2: Place the compass at A and draw an arc to cut the rays of A at B and C. Step 3: Use the same compass setting to draw an arc with P as centre, cutting l in Q Step 4: Set your compass to the length BC with the same radius. Step 5: Place the compass pointer at Q and draw the arc to cut the arc drawn earlier in R. Step 6: Join PR. This gives us P. It has the same measure as A. This means  QPR has the same measure as BAC.

Draw an angle 125 and take point A on one of its arm and B on the second arm such that OA = OB. Draw the perpendicular bisector of OA and OB. [4 MARKS]

#### SOLUTION

Solution :

Construction of angle: 1 Mark
Construction of bisector: 1 Mark
Steps: 2 Marks

i) Draw any angle 125with O as its centre.
ii) Take points A and B on its two arms. Now taking O and A as centre and radius more than half of AB draw arcs at C and D.
iii) Similarly, draw the arcs at E and F on side OB.
iv) Join CD and EF.

These are the perpendicular bisectors of OA and OB. 