CBSE Class 6 Mathematics Basic Geometrical Ideas Assignment Set 01

Worksheet - 4

Chapter - 4 (Basic Geometrical Concepts)

Question 1. Fill in the blank
i) Distance around a circle is its _______________.
Answer: circumference
In simple words: The total length of the boundary of a circle is called its circumference.

Exam Tip: Remember that perimeter for circles is specifically termed 'circumference'.

Question 1 (ii). In given line
\(AC = AB +\) _____
\(BC = BD -\) ...............
Answer: \(BC\), \(CD\)
In simple words: Line segments add up when placed end-to-end and subtract when a part is removed from the whole.

Exam Tip: Use segment addition postulate where whole length equals the sum of its non-overlapping parts.

Question 1 (iii). An angle is formed by two ____________ with same initial points called vertex.
Answer: rays
In simple words: An angle consists of two rays starting from a common endpoint.

Exam Tip: The common initial point is always the middle letter when naming the angle.

Question 2. Match the following
i) A-B (with arrows on both sides extending indefinitely)
ii) A-B (with one endpoint at A and arrow at B)
iii) A-B (with endpoints at A and B)
Options:
a) Ray
b) Line Segment
c) Line
Answer: (i) - (c), (ii) - (a), (iii) - (b)
In simple words: A line goes infinitely in both directions, a ray starts at one point and goes infinitely in one direction, and a line segment has two fixed endpoints.

Exam Tip: Look at the arrowheads carefully to distinguish between lines, rays, and line segments.

Question 3. Name the intersecting pairs of line and points of intersection.
Answer:
From the given figure with lines \(l, m, n, a, b\):
Intersecting pairs and their points of intersection:
- Line \(l\) and Line \(a\) intersect at point \(A\) (or the respective intersection node marked on vertical line \(a\)).
- Line \(l\) and Line \(b\) intersect at point \(B\) (or the intersection node on vertical line \(b\)).
- Line \(m\) and Line \(a\) intersect.
- Line \(m\) and Line \(b\) intersect.
- Line \(n\) and Line \(a\) intersect.
- Line \(n\) and Line \(b\) intersect.
In simple words: Intersecting lines cross each other at a single common point called the point of intersection.

Exam Tip: Always identify crossing lines and label the exact point where they meet.

Question 4. In the following figure, answer the questions :-
i) Name the diameter of circle ______________.
ii) Name any radius of circle _____________.
iii) Name centre of the circle _____________.
iv) Name chord of circle other than diameter _____________.
v) One interior point in the circle _____________.
vi) A point on the circle ______________ .
vii) Any exterior point of circle ______________ .
Answer:
i) \(CD\) (or line segment passing through centre \(O\) with endpoints on the circle)
ii) \(OA\) or \(OB\) or \(OC\) or \(OD\)
iii) \(O\)
iv) \(AB\)
v) \(O\) or \(M\)
vi) \(A, B, C, D\) or \(E\)
vii) \(L\)
In simple words: The diameter passes through the centre, radius connects the centre to the boundary, a chord connects any two points on the circle, and points lie inside, on, or outside the circle based on their distance from the centre.

Exam Tip: Diameter is the longest chord and is always twice the length of the radius.

Worksheet - 5

Chapter - 4 (Basic Geometrical Concepts)

Question 1. Fill in the blank
i) A triangle is a sided polygon.
ii) a quadrilateral is a ___________ sided polygon.
iii) from two points, a ________ can be drawn.
Answer:
i) 3
ii) 4
iii) line (or unique line)
In simple words: A triangle has 3 sides, a quadrilateral has 4 sides, and exactly one straight line can pass through any two distinct points.

Exam Tip: Memorize polygon names based on their number of sides (Triangle = 3, Quadrilateral = 4, Pentagon = 5, etc.).

Question 2. MCQ
i) Identify the open curve from the following :-
(a) Triangle (b) Circle (c) Trapezium (d) Wave/Arc curve
Answer: (d) [Wave/Arc open curve]
In simple words: An open curve does not enclose an area and has two distinct endpoints.

Exam Tip: Closed curves start and end at the same point, whereas open curves do not.

Question 2 (ii). Identify the polygon from the figure :-
Answer: Closed figure made of line segments (such as the triangle or quadrilateral shown in the figures).

Exam Tip: A polygon must be a simple closed curve made entirely of line segments.

Question 2 (iii). A pair of lines which don't intersect at any point :-
(a) Perpendicular lines
(b) Parallel lines
(c) Concurrent lines
(d) None
Answer: (b) parallel lines
In simple words: Parallel lines remain at the same distance apart everywhere and never meet.

Exam Tip: Perpendicular lines intersect at \(90^\circ\), while concurrent lines meet at a single common point.

Question 2 (iv). A ___________ is a mark of position.
Answer: point
In simple words: A point determines a precise location in space and has no length, width, or thickness.

Exam Tip: Points are denoted by a capital letter like \(A\), \(B\), or \(P\).

Question 3. Here is a rough sketch of a quadrilateral ABCD.
State
i) Two pairs of opposite sides ___________.
ii) Two pairs of adjacent angles ___________ .
iii) Two diagonals _______________.
Answer:
i) Pair 1: \(AB\) and \(DC\), Pair 2: \(AD\) and \(BC\)
ii) Pair 1: \(\angle A\) and \(\angle B\), Pair 2: \(\angle B\) and \(\angle C\) (or any adjacent pair)
iii) \(AC\) and \(BD\)
In simple words: Opposite sides do not meet, adjacent angles share a common arm, and diagonals connect non-consecutive vertices.

Question 4. Name the angles in the triangle
a) \(\angle ABC\)
b) ___________,
c) __________________.
Answer:
b) \(\angle BCA\) (or \(\angle C\))
c) \(\angle CAB\) (or \(\angle A\))
In simple words: A triangle has three interior angles corresponding to its three vertices.

Exam Tip: The vertex letter of the angle must always be written in the middle when using three letters.