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]
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?
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]
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]
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?
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.
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?
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.
(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)
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
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.
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.