CBSE Class 6 Mathematics Basic Geometrical Concepts Worksheet Set 07

I) Fill in the blanks :

Question 1. Circles having different radii but the same centre are called __________________
Answer: concentric circles
In simple words: Concentric circles share the same center point but have different radii.

Exam Tip: Remember that concentric circles never intersect each other.

Question 2. Radius is ________________ of the diameter.
Answer: half (\(\frac{1}{2}\))
In simple words: The radius is the distance from the center to the edge, which is half of the total diameter.

Exam Tip: Formula to remember: Radius = \(\frac{\text{Diameter}}{2}\).

Question 3. The diameter of a circle is the ________________chord of the circle.
Exam Tip: Every diameter is a chord, but not every chord is a diameter.

Question 4. The Perimeter of a circle is called the _____________________.
Answer: circumference
In simple words: The perimeter, or boundary length, of a circle has a special name called circumference.

Exam Tip: Circumference formula is \(2\pi r\) or \(\pi d\).

Question 5. A quadrilateral has ____________ diagonals.
Answer: two (2)
In simple words: Connecting opposite corners of a four-sided polygon gives two diagonals.

Question 6. A triangle has __________________elements.
Answer: six (6) (\(3\) sides and \(3\) angles)
In simple words: A triangle consists of 3 sides and 3 angles, making 6 basic elements in total.

Exam Tip: Knowing all 6 elements helps in proving triangle congruence.

Question 7. The interior of an angle together with the angle (boundary) itself is called the _______
Answer: triangular region / angle region (or region of the angle)
In simple words: The space inside an angle plus its boundary lines forms its region.

Exam Tip: Be careful to distinguish between the angle itself (the rays) and its interior region.

Question 8. In PQR, the side opposite to P is _______________
Answer: QR
In simple words: The side that does not touch vertex P is the side QR.

Exam Tip: In any triangle, the side opposite to a vertex is formed by the other two vertices.

Question 9. Length of a diameter is _________________the radius of a circle.
Answer: twice (or two times / \(2\))
In simple words: A diameter spans across the center, making it double the length of the radius.

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

Question 10. All the radii of a circle are ____________________
Answer: equal in length
In simple words: Every radius drawn from the center to any point on the circle has the exact same length.

Exam Tip: This constant distance from the center is the defining property of a circle.

II) Choose the correct answer :

Question 1. The centre of a circle
(i) Lies in its interior
(ii) Lies in its exterior
(iii) Lies on the circle
(iv) None of these
Answer: (i) Lies in its interior
In simple words: The center point is strictly inside the circle.

Exam Tip: By definition, the center is the interior reference point equidistant from the boundary.

Question 2. In quadrilateral PQRS, the two diagonals are
(i) PQ and RS
(ii) PR and RS
(iii) PS and PR
(iv) PR and QS
Answer: (iv) PR and QS
In simple words: Diagonals connect opposite vertices P to R and Q to S.

Exam Tip: Adjacent vertices form sides (PQ, QR, RS, SP), whereas non-adjacent vertices form diagonals (PR, QS).

Question 3. In the figure, the angle can be named as
(i) \(\angle OPQ\)
(ii) \(\angle POQ\)
(iii) \(\angle PQO\)
(iv) \(\angle QPO\)
Answer: (iv) \(\angle QPO\) (or \(\angle OPQ\))
In simple words: The vertex letter P must always be in the middle when naming the angle.

Exam Tip: Always write the vertex of the angle as the middle letter.

Question 4. A line segment joining any two points on the circle is called a ________________
(i) radius
(ii) diameter
(iii) chord
(iv) secant
Answer: (iii) chord
In simple words: Any line segment with both endpoints on the circle is a chord.

Exam Tip: A diameter is a special chord that passes through the center.

Question 5. A closed figure bounded by three or more segments is called a ____________
(i) Curve
(ii) Polygon
(iii) Circle
(iv) None of these
Answer: (ii) Polygon
In simple words: A closed 2D shape made of straight line segments is a polygon.

Question 6. A line intersecting a circle at two different points is called a __________________of a circle.
(i) diameter
(ii) Radius
(iii) secant
(iv) centre
Answer: (iii) secant
In simple words: A line that cuts through a circle at two points is a secant line.

Exam Tip: Distinguish between a chord (line segment) and a secant (line extending infinitely).

Question 7. A closed figure formed by joining three non-collinear points is called
(i) a triangle
(ii) an angle
(iii) a curve
(iv) none of these
Answer: (i) a triangle
In simple words: Connecting three points that do not lie on the same straight line creates a triangle.

Exam Tip: Non-collinear points are required so they do not collapse into a straight line.

Question 8. An Angle has
(i) One vertex and one arm
(ii) One vertex and two arms
(iii) Two vertex and two arms
(iv) None of these
Answer: (ii) One vertex and two arms
In simple words: An angle is formed by two rays meeting at a common endpoint called the vertex.

Exam Tip: The two rays forming the angle are called its arms or sides.

Question 9. A circle is
(i) a polygon
(ii) an open curve
(iii) a closed curve
(iv) none of these
Answer: (iii) a closed curve
In simple words: A circle is a simple closed curve where every point is equidistant from the center.

Question 10. A Point equidistant from all the Points on a circle is called the _____________of the circle.
(i) Centre
(ii) Radius
(iii) diameter
(iv) None of these
Answer: (i) Centre
In simple words: The center is the fixed middle point from which all points on the boundary are equally distant.

Exam Tip: This equidistant property is the fundamental geometric definition of a circle.

III) Additional Exercises & Solutions

Question 1. Identify triangles and figures from diagrams:
Answer:
(i) Triangles: \(\Delta RPQ, \Delta RSP, \Delta SPQ, \Delta SQR, \Delta SOP, \Delta POQ, \Delta ROQ, \Delta ROS\)
(ii) Triangles: \(\Delta ABC, \Delta ADE, \Delta EFC, \Delta DBF, \Delta ADEF\) (and sub-triangles)
(iii) Triangles: \(\Delta ABD, \Delta ADC, \Delta ABC\)
In simple words: Listing the various triangles visible in the complex geometric figures.

Exam Tip: Systematically check for smaller triangles combining into larger ones.

Question 2. For quadrilateral PQRS, state the following properties:
a) Vertices : P, Q, R, S
b) Pair of opposite sides : PQ & SR, PS & QR
c) Angles : \(\angle P, \angle Q, \angle R, \angle S\)
d) Pair of opposite angles : \(\angle P\) & \(\angle R\), \(\angle S\) & \(\angle Q\)
e) Pair of adjacent angles / sides : (Sides) PQ & QR, QR & RS, etc.
f) Diagonals : PR, SQ
Answer: As listed above in parts (a) through (f).
In simple words: Identifying fundamental parts of quadrilateral PQRS.

Exam Tip: Opposite sides do not share a common endpoint; adjacent sides share a common vertex.

Question 3. Based on the circle diagram, identify the following geometric components:
i) Centre - O
ii) A radius - OA, OB, OE, OF
iii) A diameter - AB
iv) A point in its interior - O, G
v) A point in its exterior - M, N
vi) A chord - CD
vii) An arc - EF (or arc CDF)
viii) A segment - Segment formed by chord CD and arc CD
ix) A sector - Sector formed by radii and arc
x) A point on the circle - A, B, D, F
Answer: As classified above.
In simple words: Matching circle terminology to the points and lines shown in the figure.

Exam Tip: Practice locating interior, exterior, and boundary points accurately.

Question 4. Refer to the figure showing the interior of a quadrilateral.
Answer: The shaded region bounded by vertices P, Q, R, S represents the interior of the quadrilateral PQRS.
In simple words: The space enclosed inside the four boundary segments.

Exam Tip: Points inside this region are interior points.

Question 5. Identify points and elements from diagrams:
(i) U, M, r
(ii) p, q
(iii) A, B, C, t
Answer: Elements identified from the given reference diagrams as U, M, r; p, q; and A, B, C, t.
In simple words: Listing specific points and labels indicated in the figure.

Exam Tip: Read labels carefully directly from the given figure.

Question 6. List the angles present in the given configurations:
(i) 8 Angles : \(\angle ABC, \angle BCA, \angle CAB, \angle ADC, \angle ACD, \angle CAD, \angle BAD, \angle BCD\)
(ii) 3 Angles : \(\angle QPR, \angle PRQ, \angle PQR\)
(iii) 4 Angles : \(\angle DAB, \angle ABC, \angle BCD, \angle CDA\)
Answer: As listed above for each figure.
In simple words: Naming all interior angles for the respective polygons.

Question 7. Identify angle relations from the given diagrams:
(i) \(\angle 1 = \angle ADC\), \(\angle 2 = \angle AOD\), \(\angle 3 = \angle BOC\), \(\angle 4 = \angle BOC\)
(ii) \(\angle 1 = \angle DAB\), \(\angle 2 = \angle ABD\), \(\angle 3 = \angle CBD\), \(\angle 4 = \angle BCD\), \(\angle 5 = \angle CDB\), \(\angle 6 = \angle ADB\)
(iii) \(\angle 1 = \angle ABC\), \(\angle 2 = \angle BCD\)
Answer: Angle relationships correctly mapped to standard three-letter angle notation.
In simple words: Translating numbered angle tags into precise geometric angle names.

Exam Tip: Numbered angles should always be cross-verified with the diagram to avoid naming errors.

Please refer to attached file for Basic Geometrical Ideas