# 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)