PSEB Class 6 Maths Chapter 8 Basic Geometrical Concepts Questions and Answers Solution
PSEB Punjab Board Class 6 Maths Textbook Solution Chapter 8 Basic Geometrical Concepts Questions and Answers. We have also included some Additional questions, so that students can prepare more strongly.
Exercise 8.1
1.) Give the examples of:
(i) A point
ANSWER:
Examples of a point are “tip of pencil, stars, needle end”
(ii) A line segment
ANSWER:
Examples of a line segment are “edges of tables, edges of wall”.
(iii) Parallel lines
ANSWER:
Examples of Parallel lines are “railway track, sides of eraser”.
(iv) Intersecting lines
ANSWER:
Examples of Intersecting lines are “scissors, cross roads”
(v) Concurrent lines
ANSWER:
Examples of Concurrent lines are “wheels and spokes of bicycles, spider web”
2.) Name the line segments in given line.
ANSWER:
Name of the line segments AB, AC, AD, BC, CD, BD
3.) How many lines may pass through a point?
ANSWER:
Infinite lines may pass through a point.
4.) How many points may lie on a line?
ANSWER:
Infinite points may lie on a line.
5.) How many lines pass through two points?
ANSWER:
Only One line pass through two points.
6.) Use the figure to name.
(i) Five points
ANSWER:
Five points are point O, point A, point B, point C, point D and point E.
(ii) A line
ANSWER:
Line is line BE
(iii) Four rays
ANSWER:
Four rays are ray OA, ray OB, ray OC, ray OD
(iv) Five line segments
ANSWER:
Five line segments are line segment OA, line segment OB, line segment OC, line segment OD, line segment OE, line segment DE
7.) Name the given ray in all possible ways.
ANSWER:
We have to write ray in all possible ways.
Ray PQ, ray PR, and ray QR
8.) Use the figure to name:
(i) Pair of parallel lines.
ANSWER:
Pair of parallel lines is I and m
(ii) All pairs of intersecting lines.
ANSWER:
pairs of intersecting lines are p and n, n and l, n and m, p and l, p and m.
(iii) Lines whose point of intersection is S.
ANSWER:
Lines whose point of intersection is S are m and n
(iv) Collinear points.
ANSWER:
Collinear points are P, Q, S and P, R, T
9.) Use the figure to name:
(i) All pairs of parallel lines.
ANSWER:
Pairs of parallel lines are n and p, q and p, n and q
(ii) All pairs of intersecting lines.
ANSWER:
pairs of intersecting lines are m and l, m and n, m and p, m and q, l and n, l and p, l and q
(iii) Lines whose point of intersection is D.
ANSWER:
Lines whose point of intersection is D are p and l
(iv) Point of intersection of lines m and p.
ANSWER:
Point of intersection of lines m and p is Point E.
(v) All sets of collinear points.
ANSWER:
All sets of collinear points are G, E, C, A and F, D, C, В
10.) Use the figure to name:
(i) Line containing point P.
ANSWER:
Line containing point P is l, n
(ii) Lines whose point of intersection is B.
ANSWER:
Lines whose point of intersection is B are l and m.
(iii) Point of intersection of lines m and l.
ANSWER:
Point of intersection of lines m and l is point B.
(iv) All pairs of intersecting lines.
ANSWER:
All pairs of intersecting lines are m and l, n and l.
11.) State which of the following statements are True (T) or False (F):
(i) Two lines in a plane, always intersect at a point.
ANSWER:
False.
(ii) If four lines intersect at a point, those are called concurrent lines.
ANSWER:
True.
(iii) Point has a size because we can see it as a thick dot on the paper.
ANSWER:
False.
(iv) Through a given point, only one line can be drawn.
ANSWER:
False.
(v) Rectangle is a part of the plane.
ANSWER:
True.
Exercise 8.2
1.) (a) Which of the following are simple curves?
(b) Classify the following as open or closed curve.
ANSWER:
We have to find which are simple curve
Simple curves are figure (i), (iii), (iv), (vi), (vii), (viii)
We have to find open or closed curve.
Open curves are figure (iii), (vi), (viii)
Closed curves are figure (i), (ii), (iv), (v), (vii)
2.) Identify the polygons:
ANSWER:
We have to identify which are polygons.
Polygons are figure (ii), (iii), (v).
3.) Draw any polygon and shade its interior.
ANSWER:
We have to draw any polygon and we have to shade its interior part.
4.) Name the points which are:
(i) In the interior of the closed figure.
ANSWER:
From given figure,
Points in the interior of given figure are A, B, Q
(ii) In the exterior of the closed figure.
ANSWER:
From given figure,
Points in the exterior of given figure are R, N
(iii) On the boundary of the closed figure.
ANSWER:
From given figure,
Points on the boundary of given figure are P, M
5.) In the given figure, name:
(i) The vertices
ANSWER:
From given figure,
The vertices are D, E, A, B, C
(ii) The sides
ANSWER:
From given figure,
The sides are AB, BC, CD, DE, and EA
(iii) The diagonals
ANSWER:
From given figure,
The diagonals are AC, AD, BE, BD, CE
(iv) Adjacent sides of AB
ANSWER:
From given figure,
Adjacent sides of AB are AE and BC
(v) Adjacent vertices of E.
ANSWER:
From given figure,
Adjacent vertices of E are A and D
Exercise 8.3
1.) Name the given angles in all ways:
ANSWER:
Here, we have to find all angles in all ways.
Angles are angle DEF, angle FED, angle E, angle a
ANSWER:
Here, we have to find all angles in all ways.
Angles are angle XOY, angle YOX, angle O, angle 1
ANSWER:
Here, we have to find all angles in all ways.
Angles are angle NOM, angle MON, angle O, angle x
2.) Name the vertex and the arms of given angles:
ANSWER:
Here, we have to find vertex and the arms of given angles
Vertex = B
Arm = BC, BA
ANSWER:
Here, we have to find vertex and the arms of given angles
Vertex = Q
Arm = QP, QR
ANSWER:
Here, we have to find vertex and the arms of given angles
Vertex = O
Arm = OS, OP
3.) Name all the angles of the given figure:
ANSWER:
Here, we have to find all the angles of the given figure.
Angles are Angle X, Angle Y, angle Z
ANSWER:
Here, we have to find all the angles of the given figure.
Angles are angle P, angle Q, angle R, angle S.
ANSWER:
Here, we have to find all the angles of the given figure.
Angles are angle AOB, angle BOC, angle AOC
4.) In the given figure, name the points that lie
(i) In the interior of DOE
ANSWER:
Here, we have to find interior points of Triangle DOE
Interior points of Triangle DOE = points A, X, M
(ii) In the exterior of DOE
ANSWER:
Here, we have to find exterior points of Triangle DOE.
Exterior points of Triangle DOE = points H, L
(iii) On the DOE
ANSWER:
Here, we have to find points On the Triangle DOE.
Points on the Triangle DOE = points D, B, O, E
5.) In the given figure, write another name for the following angles:
(i) Angle 1
ANSWER:
We have to write another name for Angle 1
Another name for Angle 1 = angle PSR, angle RSP, angle S
(ii) Angle 2
ANSWER:
We have to write another name for Angle 2
Another name for Angle 2 = angle RPQ or angle QPR
(iii) Angle 3
ANSWER:
We have to write another name for Angle 3
Another name for Angle 3 = angle PRS or angle SRP
(iv) Anglea
ANSWER:
We have to write another name for Angle a
Another name for Angle a = angle Q or angle RQP or angle PQR
(v) angleb
ANSWER:
We have to write another name for Angle b
Another name for Angle b = angle PRQ or angle ORP
Exercise 8.4
1.) Write all the names of the following triangles in all orders:
ANSWER:
Here, we have to write all the names of the given triangles in all orders.
Names of the given triangles = triangle ABC, triangle ACB, triangle ВАС, triangle BCA, triangle CAB, triangle CBA
ANSWER:
Here, we have to write all the names of the given triangles in all orders.
Names of the given triangles = triangle XYZ, triangle YZX, triangle YXZ, triangle ZXY, triangle ZYX, triangle XZY.
ANSWER:
Here, we have to write all the names of the given triangles in all orders.
Names of the given triangles = Triangle LMN, Triangle LNM,triangle MNL, Triangle MLN, Triangle NML, Triangle NLM.
2.) Write the name of vertices, sides and angles of the following triangles:
ANSWER:
Here, we have to write the name of vertices, sides and angles of the given triangles.
Vertices = P, R, Q
Sides = PR, QR, PQ
Angles = angle P, angle R, angle Q
ANSWER:
Here, we have to write the name of vertices, sides and angles of the given triangles.
Vertices = D, E, F
Sides = DE, EF, DF
Angles = angle D, angle E, angle F
ANSWER:
Here, we have to write the name of vertices, sides and angles of the given triangles.
Vertices = T, P, S
Sides = TP, PS, TS
Angles = angle T, angle P, angle S
3.) In the given figure, name the points that lie
(i) On the boundary of Triangle GEM
ANSWER:
We have to write points that lie on the boundary of Triangle GEM.
On the boundary of Triangle GEM = G, A, E, C, M
(ii) In the interior of Triangle GEM
ANSWER:
We have to write points that lie in the interior of Triangle GEM
In the interior of Triangle GEM = P, X, D
(iii) In the exterior of Triangle GEM
ANSWER:
We have to write points that lie in the exterior of Triangle GEM
In the exterior of Triangle GEM = Y, B
4.) In the given figure, write the name of
(i) All different triangles.
ANSWER:
We have to write names of different triangles.
triangle AOD, triangle DOC, triangle BOC, triangle AOB, triangle ABD, triangle BCD, triangle ACD ,triangle ABC
(ii) Triangles having O as the vertex.
ANSWER:
We have to write names of triangles having O as the vertex.
Triangles having O as the vertex = triangle AOB, triangle BOC, triangle COD, triangle AOD
(iii) Triangles having A as the vertex.
ANSWER:
We have to write names of Triangles having A as the vertex.
Triangles having A as the vertex = triangle AOB, triangle AOD triangle ABD, triangle ABC, triangle ACD
5.) Fill in the blanks of the following:
(i) A triangle has ———– vertices.
ANSWER:
A triangle has 3 vertices.
(ii) A triangle has ———- angles.
ANSWER:
A triangle has 3 angles.
(iii) A triangle has ———– sides.
ANSWER:
A triangle has 3 sides.
(iv) A triangle divides the plane into ———- parts.
ANSWER:
A triangle divides the plane into 3 parts.
(v) A triangle has ———– parts.
ANSWER:
A triangle has 6 parts.
Exercise 8.5
1.) Out of the following, identify the quadrilateral:
ANSWER:
From above figure the quadrilateral is
2.) Name the given quadrilaterals.
ANSWER:
We have to write name of given quadrilateral.
Name of given quadrilateral = Quadrilateral ABCD
ANSWER:
We have to write name of given quadrilateral.
Name of given quadrilateral = Quadrilateral PORS
ANSWER:
We have to write name of given quadrilateral.
Name of given quadrilateral = Quadrilateral XYZW
3.) Write the name of all vertices, angles, sides, diagonals of the following quadrilaterals:
ANSWER:
We have to write all vertices, angles, sides, diagonals of the given quadrilaterals.
Vertices = Vertices O, N, M, L
Angles = Angles M, angle O, angle N, angle, L
Sides = ON, NM, ML, LO
Diagonals = OM, NL
ANSWER:
We have to write all vertices, angles, sides, diagonals of the given quadrilaterals.
Vertices = Vertices H, G, F, E
Angles = Angles H, angle G, angle F, angle E
Sides = HG, GF, FE, EH
Diagonals = EG, FH
4.) For the given quadrilateral ABCD, name:
(i) Side opposite to AB
ANSWER:
We have to write name of Side opposite to AB
Side opposite to AB = DC
(ii) Angles adjacent to B
ANSWER:
We have to write name of angles adjacent to B
Angles adjacent to B = angle A and angle C
(iii) Diagonal joining B and D
ANSWER:
We have to write name of diagonal joining B and D
Diagonal joining B and D = BD
(iv) Angle opposite to ∠A
ANSWER:
We have to write name of Angle opposite to ∠A
Angle opposite to ∠A = angle C
(v) Sides adjacent to CD
ANSWER:
We have to write name of Sides adjacent to CD
Sides adjacent to CD = AD and BC
5.) In the given quadrilateral JUMP, name the points.
(i) In its interior
ANSWER:
We have to write name of interior points of quadrilateral JUMP.
Interior points of quadrilateral JUMP = L, N, C
(ii) In its exterior
ANSWER:
We have to write name of exterior points of quadrilateral JUMP.
Exterior points of quadrilateral JUMP = B, O, X
(iii) On its boundary
ANSWER:
We have to write name of points On boundary of quadrilateral JUMP.
Points on boundary of quadrilateral JUMP = P, M, U, Y,J,A
6.) Fill in the blanks:
(i) A quadrilateral has ——— vertices.
ANSWER: A quadrilateral has 4 vertices.
(ii) A quadrilateral has ————- sides.
ANSWER:
A quadrilateral has 4 sides.
(iii) A quadrilateral has ———- angles.
ANSWER:
A quadrilateral has 4 angles.
(iv) A quadrilateral has —————– diagonals.
ANSWER:
A quadrilateral has 2 diagonals.
(v) A diagonal divides the quadrilateral into ————— triangles.
ANSWER:
A diagonal divides the quadrilateral into 2 triangles.
(vi) A line segment joining the opposite vertices of a quadrilateral is called its ———————
ANSWER:
A line segment joining the opposite vertices of a quadrilateral is called its diagonal.
(vii) The interior and the boundary of a quadrilateral together constitute the ———– region.
ANSWER:
The interior and the boundary of a quadrilateral together constitute the quadrilateral region.
7.) State True or False:
(i) A diagonal divides quadrilateral into four triangles.
ANSWER:
False.
(ii) The angle that have a common vertex are called adjacent angles.
ANSWER:
False.
(iii) The sides that have a common vertex are called adjacent sides.
ANSWER:
True.
(iv) A quadrilateral has four diagonals.
ANSWER:
False.
(v) The quadrilateral region consists of the exterior and the boundary of the quadrilateral.
ANSWER:
False.
Exercise 8.6
1.) In the given figure, write the name of
(i) Centre
ANSWER:
We have to write name of Centre of circle.
Centre of circle = O
(ii) Radii
ANSWER:
We have to write name of Radii of circle.
Radii of circle = OP, OX, ΟΥ
(iii) Diameter
ANSWER:
We have to write name of Diameter of circle.
Diameter of circle = XY
(iv) Chord
ANSWER:
We have to write name of Chord of circle.
Chord of circle = XY and QR
2.) In the given figure, write the name of
(i) Minor arc
ANSWER:
We have to write name of Minor arc of circle
Minor arc of circle = PAQ
(ii) Major arc
ANSWER:
We have to write name of Major arc of circle
Major arc of circle = PBQ
(iii) Minor sector
ANSWER:
We have to write name of Minor sector of circle
Minor sector of circle = OPAQ
(iii) Major sector
ANSWER:
We have to write name of Major sector of circle
Major sector of circle = OPBQ
3.) In the given figure, write the name of
(i) Minor segment
ANSWER:
We have to write name of Minor segment of circle
Minor segment of circle = ACBA
(ii) Major segment
ANSWER:
We have to write name of Major segment of circle
Major segment of circle = ADBA
4.) In the given figure, name the points
(i) In its interior
ANSWER:
We have to write name of interior points in the given circle.
Interior points in the given circle = A, O, F, D
(ii) On its boundary (circumference)
ANSWER:
We have to write name of points on boundary of the given circle.
Points on boundary of the given circle = C
(iii) In its exterior
ANSWER:
We have to write name of exterior points in the given circle.
Exterior points in the given circle = B, E
5.) Find the diameter of the circle whose radius is
(i) 5cm
ANSWER:
We know,
Diameter of the circle = 2 x Radius
Diameter of the circle = 2 x 5cm
Diameter of the circle = 10 cm
(ii) 4m
ANSWER:
We know,
Diameter of the circle = 2 x Radius
Diameter of the circle = 2 x 4m
Diameter of the circle = 8 m.
(iii) 10cm
ANSWER:
We know,
Diameter of the circle = 2 x Radius
Diameter of the circle = 2 x 10 cm
Diameter of the circle = 20 cm
6.) If the diameter of a circle is 12cm. Find the radius.
ANSWER:
Here given, diameter of a circle is 12cm.
We know,
Diameter of the circle = 2 x Radius
Radius = Diameter of the circle / 2
Radius = 12cm / 2
Radius = 6 cm.
7.) Fill in the blanks:
(i) The distance around a circle is called ———-
ANSWER:
The distance around a circle is called Circumference
(ii) The diameter of a circle is ——— times its radius.
ANSWER:
The diameter of a circle is 2 times its radius.
(iii) The longest chord of circle is —————-
ANSWER:
The longest chord of circle is Diameter.
(iv) All the radii of a circle are of ————– length.
ANSWER:
All the radii of a circle are of equal length.
(v) The diameter of a circle passes through —————-
ANSWER:
The diameter of a circle passes through centre.
(vi) A circle divides all the points in a plane into —————– parts.
ANSWER:
A circle divides all the points in a plane into 3 parts.
8.) State true or false:
(i) The diameter of a circle is equal to its radius.
ANSWER:
False.
(ii) The diameter is a chord of circle.
ANSWER:
True.
iii) A radius is a chord of the circle.
ANSWER:
False.
(iv) Every circle has a centre.
ANSWER:
True.
(v) The region enclosed by a chord and arc is called a segment.
ANSWER:
True.
Multiple Choice Questions
1.) How many lines can pass through a point?
(a) 1
(b) 2
(c) 3
(d) Infinite
ANSWER: (d) Infinite
2.) The number of points lie on a line are
(a) 2
(b) 4
(c) 1
(d) Infinite
ANSWER: (d) Infinite
3.) The number of lines passes through two points are
(a) 1
(b) 2
(c) 4
(d) Infinite
ANSWER: (a) 1
4.) In how many parts, a closed curve divides the plane?
(a) 1
(b) 2
(c) 3
(d) 4
ANSWER: (c) 3
5.) A quadrilateral has —- diagonals.
(a) 1
(b) 2
(c) 3
(d) 4
ANSWER: (b) 2
6.) Which of the following is not a polygon?
(a) Triangle
(b) Pentagon
(c) Circle
(d) Quadrilateral
ANSWER: (c) Circle
7.) A triangle has …………..parts.
(a) 3
(b) 6
(c) 9
(d) 2
ANSWER: (b) 6
8.) Which of the following is not a quadrilateral?
ANSWER: b
9.) A line segment joining the opposite vertices of a quadrilateral is called its
(a) Diagonal
(b) Side
(c) Angle
(d) Region
ANSWER: (a) Diagonal
10.) The radius of a circle is 4cm then the diameter is
(a) 8cm
(b) 2cm
(c) 6cm
(d) 12cm
ANSWER: (a) 8cm
11.) The diameter of a circle is 12cm then the radius is
(a) 24cm
(b) 6cm
(c) 18cm
(d) 4cm
ANSWER: (b) 6cm
12.) The longest chord of a circle is
(a) Arc
(b) Perimeter
(c) Diameter
(d) Radius
ANSWER: (c) Diameter
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