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

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.

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.

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.

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.

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:
Hence there 10 lines segments in the above figure.

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.

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.

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)

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

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)