CBSE Class 6 Mathematics Basic Geometrical Concepts Worksheet Set 13

Basic Geometrical Ideas

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1. Fill in the blanks

Question 1(1). The boundary of a circle is __________.
Answer: circumference
In simple words: The total length of the boundary of a circle is called its circumference.

Exam Tip: Remember that perimeter of a circle has a special name, circumference.

Question 1(2). The interior of a triangle along with its boundary is called ______.
Answer: triangular region
In simple words: The inside space plus the boundary lines make up the triangular region.

Exam Tip: Distinguish between the triangle (only the three boundary segments) and the triangular region (interior plus boundary).

Question 1(3). A _______ has its end - point on the circle
Answer: radius (or ray starting from the center)
In simple words: A radius is a line segment connecting the center to any point on the boundary of the circle.

Exam Tip: The center is inside the circle, and the other endpoint lies directly on the circle.

Question 1(4). Lines which never meet are ______ lines
Answer: parallel
In simple words: Parallel lines stay the same distance apart and never intersect.

Exam Tip: Railway tracks are a classic real-life example of parallel lines.

Question 1(5). Closed figure made of line segments _______.
Answer: polygon
In simple words: Any closed 2D shape formed strictly by straight line segments is called a polygon.

Question 2.1. What are the end points of the line segment
Answer: A and B (referring to the standard line segment figure with points A and B)
In simple words: A line segment starts at one fixed point and ends at another.

Exam Tip: Always denote a line segment with its two endpoints, such as segment \(AB\).

Question 2.2. Is C the end point of ray
Answer: No, C is a point lying on the ray or line, but the starting fixed point (endpoint) of a ray is its origin.
In simple words: A ray has only one starting endpoint, and other points lie along its infinite path.

Exam Tip: The starting point is the sole endpoint of a ray.

Question 2.3. Which of the points lie on the line
Answer: All points marked along the straight path (e.g., A, B, C, D, E depending on the referenced figure)
In simple words: Points that fall directly on the straight path are said to lie on that line.

Exam Tip: Collinear points lie on the same straight line.

Question 2.4. Fill in the blank. If given line: (i) AC = AB + ____ (ii) BC = BD -___.
Answer: (i) BC (ii) CD
In simple words: Line segments add up when placed end-to-end along a straight line.

Exam Tip: Use segment addition postulate: if B is between A and C, then \(AC = AB + BC\).

Question 2.5. How many points are there actually in a line
Answer: Infinite points
In simple words: A line is made up of an endless number of points packed closely together.

Question 3. Circumference of a circle is equal to
(A) \(r\)
(B) \(2\pi r\)
(C) \(\pi\)
(D) \(2 + \frac{\pi}{2}r\)
Answer: (B) \(2\pi r\)
The formula for the circumference of a circle of radius \(r\) is \(2\pi r\).
In simple words: Circumference is calculated as 2 times pi times the radius.

Exam Tip: Alternatively, circumference can be written as \(\pi d\) where \(d\) is the diameter.

Question 4. Symbol to represent an arc is
(A) \(\perp\)
(B) \(||\)
(C) \(\frown\)
(D) \(\square\)
Answer: (C) \(\frown\)
An arc of a circle is symbolically denoted by a curved cap symbol placed over the letters, such as \(\overparen{AB}\).
In simple words: A curved line above the letters represents an arc.

Exam Tip: \(\perp\) means perpendicular, \(||\) means parallel.

Question 5. Value of \(\pi\) is equal to (approximately)
(A) 3.41
(B) 3.14
(C) \(\frac{23}{7}\)
(D) \(\frac{21}{7}\)
Answer: (B) 3.14
The mathematical constant \(\pi\) is approximately equal to \(3.14159\) or \(\frac{22}{7}\).
In simple words: Pi is approximately 3.14.

Question 6. A line PQ is symbolically written as
(A) \(\overline{PQ}\)
(B) \(\overleftrightarrow{PQ}\)
(C) PQ
(D) \(\widehat{PQ}\)
Answer: (B) \(\overleftrightarrow{PQ}\)
A line extends indefinitely in both directions and is denoted by arrows on both sides over the points.
In simple words: A line has double arrows on top.

Exam Tip: \(\overline{PQ}\) represents a line segment, and \(\overrightarrow{PQ}\) represents a ray.

Question 7. If the diameter of a circle is 14 cm, then its circumference is
(A) 66 cm
(B) 44 cm
(C) 33 cm
(D) 55 cm
Answer: (B) 44 cm
Diameter \(d = 14\) cm.
Circumference = \(\pi d = \frac{22}{7} \times 14 = 22 \times 2 = 44\) cm.
In simple words: Multiply pi by the diameter to get 44 cm.

Exam Tip: Always include proper units (cm) in your final answer.

Question 8. Diameter of a circle is 7.12 cm, then its radius is
(A) 35.6 cm
(B) 3.56 cm
(C) 356 cm
(D) 0.356 cm
Answer: (B) 3.56 cm
Radius \(r = \frac{\text{Diameter}}{2} = \frac{7.12}{2} = 3.56\) cm.
In simple words: Radius is always half of the diameter.

Question 9. 3 cm; \(\overline{RS} = 6.2\) cm, then the measure of line segment whose length is equal to sum of PQ and \(\overline{RS}\) is
(A) 3.2 cm
(B) 4 cm
(C) 4.2 cm
(D) 9.2 cm
Answer: (D) 9.2 cm
Length of PQ = 3 cm
Length of \(\overline{RS}\) = 6.2 cm
Sum = \(3\text{ cm} + 6.2\text{ cm} = 9.2\text{ cm}\).
In simple words: Add the two lengths together: \(3 + 6.2 = 9.2\).

Question 10. In the given figure, points A, O and B are called
(A) collinear
(B) non-collinear
(C) concurrent
(D) None of the options
Answer: (A) collinear
Points that lie on the same straight line are called collinear points.
In simple words: Points on the same straight line are collinear.

Question 11. An area bounded by chord and major arc is called
(A) minor segment
(B) major arc
(C) major segment
(D) semicircle
Answer: (C) major segment
The region bounded by a chord and the major arc is the major segment of the circle.
In simple words: The larger region cut off by a chord is the major segment.

Exam Tip: A chord divides a circle into two segments: minor and major.

Question 12. Each half equal part of the circle is called
(A) semicircle
(B) major circle
(C) minor circle
(D) none
Answer: (A) semicircle
A diameter divides a circle into two equal halves, each known as a semicircle.
In simple words: Half of a circle is a semicircle.

Exam Tip: A semicircle is bounded by a diameter and a half-circle arc.

Question 13. Number of radii that can be drawn on a circle are
(A) 2
(B) more than 1 but less than 7
(C) many
(D) None of the options
Answer: (C) many (infinite)
A circle consists of an infinite number of points on its boundary, so an infinite number of radii can be drawn.
In simple words: You can draw countless radii from the center to the circle.

Exam Tip: All radii of the same circle are equal in length.

Question 14. Number of arcs made by a chord on a circle are
(A) 3
(B) 2
(C) one
(D) none
Answer: (B) 2
A chord divides the circle boundary into two arcs: a minor arc and a major arc.
In simple words: A chord splits the circle's edge into two arc sections.

Question 15. Longest chord of the circle is
(A) Diameter
(B) Chord
(C) Radius
(D) None of the options
Answer: (A) Diameter
The diameter is a chord that passes through the center of the circle and is the longest possible chord.
In simple words: The diameter is the biggest chord in any circle.

Exam Tip: Diameter = \(2 \times \text{radius}\).

Question 16. The interior and boundary of a triangle is called
(A) exterior
(B) interior
(C) triangular region
(D) plane
Answer: (C) triangular region
The combination of the interior points and the boundary points forms the triangular region.
In simple words: The inside plus the boundary makes the triangular region.

Exam Tip: A triangle itself is only the three boundary line segments.

Question 17. Line n is parallel to line m. Symbolically, above statement is written as
(A) n - m
(B) n || m
(C) n = m
(D) none
Answer: (B) n || m
Parallel lines are denoted using the double vertical bars symbol (\(||\)).
In simple words: Two vertical lines mean parallel.

Question 18. The common end point of an angle is called
(A) vertex
(B) Zero
(C) end point
(D) None of the options
Answer: (A) vertex
The two rays forming an angle originate from a common fixed point called the vertex.
In simple words: The corner point where two rays meet is the vertex.

Exam Tip: When naming an angle, the vertex letter is always written in the middle (e.g., \(\angle ABC\)).

Question 19. Which of the following statement is true?
(A) Every ray has a definite length.
(B) Every line has a definite length.
(C) Every line segment has a definite length.
(D) None of the options.
Answer: (C) Every line segment has a definite length.
A line segment has two fixed endpoints, meaning its length can be measured exactly.
In simple words: Only line segments have a fixed, measurable length.

Exam Tip: Lines and rays extend infinitely and do not have a definite length.

Question 20. A line segment has two end points. How many lines can be drawn that pass through two different points?
(A) 1
(B) 2
(C) 3
(D) Infinite
Answer: (A) 1
Through any two distinct points, exactly one unique line can be drawn.
In simple words: Only one straight line can pass through two given points.

Question 21. A line segment has _____ end points
(A) one
(B) two
(C) three
(D) none
Answer: (B) two
By definition, a line segment is bounded by two distinct endpoints.
In simple words: A line segment has exactly two endpoints.

Exam Tip: Rays have 1 endpoint, lines have 0 endpoints.

Question 22. Number of lines that can be drawn from two distinct points on a plane
(A) two
(B) one
(C) zero
(D) infinite
Answer: (B) one
Only one unique straight line passes through two distinct points.
In simple words: Exactly one line connects two points.

Exam Tip: Two points determine a unique line.

Question 23. Number of end points in a line segment are
(A) three
(B) none
(C) two
(D) one
Answer: (C) two
A line segment has two fixed endpoints.
In simple words: A line segment has 2 endpoints.

Exam Tip: Endpoints mark the start and end of the segment.

Question 24. A set of points with one end point and can be extended in other direction is
(A) line segment
(B) line
(C) ray
(D) none
Answer: (C) ray
A ray starts at a fixed point and extends infinitely in one direction.
In simple words: A ray has one endpoint and goes on forever in the other direction.

Exam Tip: Sunlight rays are a physical analogy (starting at the sun, extending outward).

Question 25. A Figure having no length, breadth or height
Answer: Point
In simple words: A point is a zero-dimensional geometric object representing position.

Exam Tip: A point has position but no dimensions.

Question 26. A Figure which can extend endlessly in both direction?
Answer: Line
In simple words: A line goes on forever in both directions.

Exam Tip: Represented with arrows on both ends.

Question 27. A portion of a line having two end-points.
Answer: Line segment
In simple words: A piece of a line with two fixed ends is a line segment.

Exam Tip: Line segments can be measured with a ruler.

Question 28. A Figure Having one end- point and the other portion can extends infinitely.
Answer: Ray
In simple words: A ray starts at one point and extends endlessly.

Question 29. Lines which have a point in Common
Answer: Intersecting lines
In simple words: Lines that cross each other share a common intersection point.

Exam Tip: The common point is called the point of intersection.

Question 30. Lines which have no points in common.
Answer: Parallel lines
In simple words: Parallel lines never cross, so they share no points.

Exam Tip: Distance between parallel lines remains constant.

Question 31. [___] is the longest Chord of the Circle
Answer: Diameter
In simple words: The diameter passes through the center and is the longest chord.

Exam Tip: Every diameter is a chord, but not every chord is a diameter.

Question 32. All the Radii of circles are _____
Answer: equal in length
In simple words: Every radius in the same circle has the exact same length.

Exam Tip: This is a defining property of a circle.

Question 33. A Triangle has _____ angles.
Answer: three
In simple words: A triangle is a 3-sided polygon with 3 angles.

Exam Tip: The sum of all three interior angles in a triangle is always 180 degrees.

Question 34. The boundary of a circle is _______________.
Answer: circumference
In simple words: The curved boundary is called the circumference.

Exam Tip: Circumference equals \(2\pi r\).

Question 35. The interior of a triangle along with its boundary is called _______.
Answer: triangular region
In simple words: Inside plus boundary equals the triangular region.

Exam Tip: Useful when calculating area.

Question 36. A ______ has its end - points on the circle.
Answer: chord
In simple words: A line segment joining any two points on a circle is a chord.

Exam Tip: Diameter is the longest chord.

Question 37. Closed figure made of line segments is called ________.
Answer: polygon
In simple words: A closed shape made of straight line segments is a polygon.

Exam Tip: Must be closed and formed by straight segments.

Question 38. Intersection point of two diameters of a circle is called.
Answer: center of the circle
In simple words: The point where two diameters cross is the center.

Exam Tip: All diameters intersect at the circle's center.

Question 39. If the radius of the circle is 7 cm, then the circumference of that circle is...
(A) 22 cm.
(B) 44 cm.
(C) 44 m.
(D) 44 dm.
Answer: (B) 44 cm.
Radius \(r = 7\) cm.
Circumference = \(2\pi r = 2 \times \frac{22}{7} \times 7 = 44\) cm.
In simple words: Calculate \(2 \times \frac{22}{7} \times 7 = 44\) cm.

Exam Tip: Watch out for units; radius is in cm, so circumference is in cm.

Question 40. A point has
(A) A length
(B) A breadth
(C) Both
(D) No length, breadth or no thickness
Answer: (D) No length, breadth or no thickness
A point is a dimensionless location in space.
In simple words: A point has zero dimensions.

Exam Tip: It only indicates position.

Question 41. How many points are on a line?
(A) 2
(B) Infinite
(C) 3
(D) 0
Answer: (B) Infinite
A line consists of infinitely many points.
In simple words: Countless points make up a line.

Exam Tip: Lines are continuous sets of points.

Question 42. A line segment has definite
(A) Breadth
(B) Thickness
(C) Length
(D) None
Answer: (C) Length
A line segment has a fixed, measurable length.
In simple words: You can measure the length of a line segment.

Exam Tip: It has no breadth or thickness, only length.

Question 43. In the given figure, lines l, m and n intersect at point O. Can we draw any more lines through O? If yes, how many?
(A) No
(B) 1
(C) Infinite
(D) None of these.
Answer: (C) Infinite
An infinite number of lines can pass through a single given point O.
In simple words: You can draw countless lines through one point.

Exam Tip: While two points determine 1 line, one point allows infinite lines.

Question 44. How many lines can be drawn passing through two distinct points?
(A) Two lines
(B) Three lines
(C) One unique line
(D) Infinite
Answer: (C) One unique line
Only one straight line can pass through any two distinct points.
In simple words: Exactly one line connects two points.

Exam Tip: Fundamental geometric axiom.

Question 45. How many lines can be drawn passing through four collinear points?
(A) Infinite
(B) Two
(C) Three
(D) One
Answer: (D) One
Since all four points are collinear (lie on the same line), only one unique line passes through them.
In simple words: Collinear points all lie on the same single line.

Exam Tip: Collinear means lying on the same line.

Question 46. In the given figure, name the lines which are concurrent.
(A) l, m, n
(B) l, m, n and p
(C) l, m
(D) None of these.
Answer: (B) l, m, n and p (based on standard concurrent line diagrams passing through point A)
Concurrent lines are three or more lines that pass through the same single point.
In simple words: Lines meeting at one common point are concurrent.

Exam Tip: Check if all listed lines intersect at the exact same point.

Question 47. The diameter of the circle is-
(A) Twice the radius.
(B) Half the radius.
(C) Equal to the radius.
(D) None.
Answer: (A) Twice the radius.
Diameter = \(2 \times r\).
In simple words: Diameter is two times the radius.

Exam Tip: \(d = 2r\).

Question 48. How many line segments are there in the given figure? (PQRS quadrilateral with diagonals)
(A) 4
(B) 3
(C) 2
(D) 1
Answer: (A) 4 (or more if diagonals are included, typically 4 sides: PQ, QR, RS, SP)
In simple words: Counting the boundary line segments gives 4.

Exam Tip: Count each distinct side segment carefully.

Question 49. Which out of the following statements is true?
(A) A line segment has no length.
(B) A line segment has one end only.
(C) A line segment has breadth.
(D) A line segment has length.
Answer: (D) A line segment has length.
A line segment has two endpoints and a definite, measurable length.
In simple words: Line segments have a specific length.

Exam Tip: It has two endpoints, not one.

Question 50. Two line segments of the same length are said to be………….
(A) Parallel.
(B) Congruent.
(C) Both.
(D) None.
Answer: (B) Congruent.
Line segments of equal length are geometrically congruent.
In simple words: Equal length segments are congruent.

Exam Tip: Symbol for congruence is \(\cong\).

Question 51. The difference between a line and a line segment is-
(A) A line has indefinite length and a line segment has definite length.
(B) A line has definite length and a line segment has indefinite length.
(C) A line has no length and a line segment has breadth.
(D) No difference between line and line segment.
Answer: (A) A line has indefinite length and a line segment has definite length.
Lines extend endlessly in both directions (indefinite), while line segments have two endpoints (definite).
In simple words: Lines go on forever; segments have fixed ends and length.

Exam Tip: Remember: Line = infinite; Line segment = finite.

Question 52. In the given figure, interior points are…….
(A) M, S, X
(B) L, R, Z
(C) A, P, T
(D) None of these.
Answer: (A) M, S, X (based on standard triangle/angle interior region markings)
Points lying inside the boundary of the figure are interior points.
In simple words: Points inside the shape are interior points.

Exam Tip: Check whether points are inside, on, or outside the boundary.

Question 53. An angle which is greater than a straight angle but less than a complete angle is called a/an-
(A) Acute angle.
(B) Obtuse angle.
(C) Straight angle.
(D) Reflex angle.
Answer: (D) Reflex angle.
An angle measuring between \(180^{\circ}\) and \(360^{\circ}\) is a reflex angle.
In simple words: Angles between 180 and 360 degrees are reflex angles.

Exam Tip: Acute \(< 90^{\circ}\), Obtuse \(> 90^{\circ}\) and \(< 180^{\circ}\), Straight \(= 180^{\circ}\).

Question 54. Two angles are said to be adjacent if they have……
(A) Same vertex and a common arm.
(B) Same vertex, a common arm and the other two arms on the opposite sides of the common arm.
(C) Neither same vertex nor a common arm.
(D) None of these.
Answer: (B) Same vertex, a common arm and the other two arms on the opposite sides of the common arm.
Adjacent angles share a common vertex and common arm, with non-common arms on opposite sides.
In simple words: Adjacent angles sit side-by-side sharing a vertex and a middle ray.

Exam Tip: They must not overlap.

Question 55. Which out of the following statements is true?
(A) A ray has two end-points.
(B) Every ray has finite length.
(C) The ray AB is same as the ray BA.
(D) The ray OA extends endlessly towards A.
Answer: (D) The ray OA extends endlessly towards A. (or ray starting from O through A)
A ray has one starting endpoint and extends infinitely in the direction of the second point.
In simple words: Ray OA starts at O and goes infinitely past A.

Exam Tip: Ray AB and ray BA are not the same because their starting points differ.

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Question 56. Which is the common arm of \(\angle DOE\) & \(\angle FOE\)
Answer: Ray OE (or \(\overrightarrow{OE}\))
In simple words: The ray OE is shared by both angles.

Exam Tip: The common arm is the ray that is part of both adjacent angles.

Question 57. Name the points lying in the interior and exterior of \(\angle DOE\).
Answer: Interior points: K (and E depending on diagram region). Exterior points: J, F.
In simple words: Points inside the opening are interior; points outside are exterior.

Question 58. In the following figure identify: 1) Any three angles. 2) Name the common Vertex 3) Name the three rays
Answer:
1) Three angles: \(\angle DOE\), \(\angle FOE\), \(\angle DOF\)
2) Common vertex: O
3) Three rays: \(\overrightarrow{OD}\), \(\overrightarrow{OE}\), \(\overrightarrow{OF}\)
In simple words: Identify angles, the shared vertex point, and the radiating rays.

Exam Tip: Always list rays starting from the vertex point O.

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Question 59. (a) Identify three triangles in the given figure (with vertices P, Q, S, R)
(b) Write the names of seven angles
(c) Write then names of 6 line segments
Answer:
(a) Three triangles: \(\triangle PQS\), \(\triangle PSR\), \(\triangle PQR\)
(b) Seven angles: \(\angle PQS\), \(\angle PSQ\), \(\angle QPS\), \(\angle PSR\), \(\angle PRS\), \(\angle RPS\), \(\angle QPR\) (or \(\angle QPR\), \(\angle PQR\), \(\angle PRQ\), \(\angle PSQ\), \(\angle PSR\), \(\angle RPS\), \(\angle SPQ\))
(c) Six line segments: PQ, QR, RS, SP, PS, QS (or specific distinct segments formed in the triangulated figure: PQ, QS, SR, PR, PS, QR)
In simple words: Break down the complex figure into individual triangles, angles, and line segments.

Exam Tip: Be systematic when listing geometric components to avoid repetition or omission.

Question 60. (a) line containing point 's'
(b) lines passing through X
(c) Line on which 'R' lies
(d) Two pairs of intersecting lines
Answer:
(a) Line containing point S: line \(s\) (or line passing through S)
(b) Lines passing through X: lines \(l\) and \(m\) (based on given intersecting line diagram)
(c) Line on which R lies: line \(m\) or line \(p\)
(d) Two pairs of intersecting lines: Line \(l\) and Line \(m\); Line \(m\) and Line \(n\)
In simple words: Inspect the diagram to find which lines pass through or intersect at specific points.

Exam Tip: Trace each line carefully using its given label name (\(l\), \(m\), \(n\), \(p\)).

Question 61. In the given figure (Triangle ABC):
1) Name the figure formed
2) Name the three vertices
3) Name the three sides
4) Name the three angles
5) Name the side opposite to vertex A and the side opposite to vertex C
Answer:
1) Triangle (\(\triangle ABC\))
2) Three vertices: A, B, C
3) Three sides: \(\overline{AB}\), \(\overline{BC}\), \(\overline{CA}\)
4) Three angles: \(\angle A\) (or \(\angle CAB\)), \(\angle B\) (or \(\angle ABC\)), \(\angle C\) (or \(\angle BCA\))
5) Side opposite to vertex A is \(\overline{BC}\); side opposite to vertex C is \(\overline{AB}\).
In simple words: A triangle has 3 vertices, 3 sides, and 3 angles. The side opposite a vertex does not touch that vertex.

Exam Tip: Opposite side to a vertex is formed by the other two vertices.

Question 62. In the given quadrilateral MNOP identify:
a) Two pairs of opposite sides
b) Four pairs of adjacent sides
c) 2 pairs of opposite angles
d) 2 diagonals
e) Any two pair of adjacent angles
Answer:
a) Two pairs of opposite sides: MN and PO; MP and NO
b) Four pairs of adjacent sides: (MN, NO), (NO, OP), (OP, PM), (PM, MN)
c) Two pairs of opposite angles: \(\angle M\) and \(\angle O\); \(\angle N\) and \(\angle P$
d) Two diagonals: \(\overline{MO}\) and \(\overline{NP}\)
e) Any two pairs of adjacent angles: (\(\angle M\), \(\angle N\)) and (\(\angle N\), \(\angle O\))
In simple words: Opposite sides/angles face each other; adjacent sides/angles share a common vertex or side.

Question 63. The given figure is a circle with centre 'O'. Identify:
(i) Radius (any four)
(ii) Diameter of the circle
(iii) 2 chords
(iv) Sector of the circle
(v) Segment of the circle.
Answer:
(i) Four radii: OA, OB, OC, OL (or OE)
(ii) Diameter: AB (or any chord passing through center O)
(iii) Two chords: AB, BC (or any line segment joining two points on the circle)
(iv) Sector of the circle: Region enclosed by radii OA and OB and arc AB (e.g., sector AOB)
(v) Segment of the circle: Region bounded by chord BC and arc BC
In simple words: Radii go from center to edge; chords connect two edge points; sectors use radii; segments use chords.

Question 64. Define and Explain with figures.
1. POINT 2. LINE 3. LINE SEGMENT 4. RAY 5. INTERSECTING LINES
Answer:
1. POINT: A point determines a location and has no length, width, or thickness. Represented by a fine dot.
2. LINE: A line is a straight path that extends indefinitely in both directions without any endpoints.
3. LINE SEGMENT: A portion of a line with two distinct endpoints and a fixed length.
4. RAY: A portion of a line that starts at one fixed endpoint and extends endlessly in one direction.
5. INTERSECTING LINES: Two or more lines that cross each other at exactly one common point called the point of intersection.
In simple words: These are the fundamental building blocks of geometry.

Exam Tip: Draw clear neat diagrams with proper arrowheads and labels for each definition.