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)