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

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?

[2 MARKS]

SOLUTION

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

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

Solution :

Drawing figures: 2 Marks
Reason: 1 Mark

In ∠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?


[3 MARKS]

SOLUTION

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:
AB,AC,AD,AE,BC,BD,BE,CD,CE,DE.
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.


[3 MARKS]

SOLUTION

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?


[4 MARKS]

SOLUTION

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?


[4 MARKS]

SOLUTION

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





[4 MARKS]

SOLUTION

Solution :

Each option: 0.5 Marks

(a)  ∠ ABD   
(b)   ∠ RTS 
(c)  ∠ ACD and  ∠ ACB
(d)   ∠ RTW and  ∠ RTS
(e)   ∠ AED,  ∠ AEB,  ∠ BEC and  ∠ DEC
 (f)   ∠ AEC
(g)   ∠ ACD
(h)   ∠ AKO, ∠ AKP,  ∠ BKO,  ∠ BKP

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.

[4 MARKS]

SOLUTION

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.

(d)   

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