Free Basic Geometrical Ideas Subjective Test 01 Practice Test - 6th grade 

Question 1

What do you understand by sector of a circle? Explain with a figure. [1 MARK]


Solution :

A circular sector or circle sector (symbol:), is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger area is the major sector. In the diagram, θ is the central angle in radians, r is the radius of the circle, and L is the arc length of the minor sector.

Question 2

How many lines can pass through

1. One given point?

2. Two given points?



Solution :

Each Point: 1 Mark

1. An infinite number of lines can pass through one given point.

2. Only one line can pass through two given points. 

Question 3

Sushma did not understand the difference between line and line segment. Explain both with the help of figure. [2 MARKS]


Solution :

Definition: 1 Mark
Solution: 1 Mark

A line segment is a piece, or part, of a line in geometry.

A line segment is represented by endpoints on each end of the line segment.

A line in geometry is represented by a line with arrows at each end.

A line segment and a line are different because a line goes on forever while a line segment has a distinct beginning and end.

Question 4

Draw ABC. How is it different from BAC? Show with a figure. [3 MARKS]


Solution :

Drawing figures: 2 Marks
Reason: 1 Mark

ABC we use two lines AB and BC to make B whereas in BAC we use lines BA and AC to make angle A.


Question 5

What is a line-segment? What is a ray? How many line segments can be made out of the following line?



Solution : Line segment: 1 Mark
Ray: 1 Mark
Number of Lines segments: 1 Mark

In a line segment, the endpoints are fixed i.e. a line is contained between two points.

A ray is a portion of a line. It starts at one point and goes endlessly in one direction.

The line segments in the above figure are:
Hence there 10 lines segments in the above figure.

Question 6

In the given fig., name the points lying,
a)The exterior of the Triangle QPR
b)The interior of the Triangle QPR
c)The triangle QPR itself.



Solution : Each option: 1 Mark
The points that are lying inside the triangle are  O, S
The points that are lying outside the triangle are T and N.
The only point that lies on the triangle is M.

Question 7

Will the measure of ABC and of  CBD make the measure of  ABD in the given figure? Name all the rays in the figure. Which of the two angles share a common ray?



Solution :

Explanation: 1 Mark
Solution: 1 Mark
Naming of Rays: 1 Mark
Common Ray: 1 Mark

In  ABC and  CBD, BC is a common arm. So,  ABC and  CBD form a linear pair.
Hence,  ABC +  CBD =  ABD.
The various rays in the above figure are BA, BC, BD.

The two angles that share a common ray are ABC and CBD.

Question 8

In fig.

(a)  What is AE + EC?

(b)  What is AC – EC?

(c)  What is BD – BE?

(d)  What is BD – DE?



Solution : Each point: 1 Mark

(a)  In line segments AE and EC, point E is a common point
So, AE + EC = AC
(b)   In part (a) we have proved that:
AE + EC = AC
AC – EC = AE

(c)  For line segments BE and ED, point E is a common point.
So,   BE + ED = BD
  BE – BE = ED

(d)  Also, BE = BE + ED
BD – DE = BE   
( line segment ED = line segment DE)

Question 9

Using the information given, name the right angles in each part of the given figures:
(a)   BA  BD

(b)   RT ST

(c)   AC BD

(d)  RS RW

(e)   AC BD

(f)   AE CE

(g)  AC  CD

(h)   OP AB



Solution :

Each option: 0.5 Marks

(a)  ABD   
(c)  ACD and  ACB
RTW and  RTS
AED,  AEB,  BEC and  DEC

Question 10

In Fig. alongside, O is the centre of the circle.

(a)  Name all chords of the circle

(b)   Name all radii of the circle.

(c)  Name a chord, which is not the diameter of the circle.

(d)  Shade sectors OAC and OPB.



Solution :

Each option: 1 Mark

(a)  CP and AB are two chords of the circle.

(b)  OP, OC, OA and OB are all radii of the circle.

(c)  CP is a chord of the circle, which is not a diameter.