CBSE Class 6 Mathematics Basic Geometrical Concepts Worksheet Set 08

Question 1. Draw a circle and mark the following :
a) centre b) radius c) diameter d) 2 chords
Answer:
To draw a circle and mark the required parts:
1. Draw a circle using a compass with a fixed centre point \(O\).
2. Mark the fixed point as centre \(O\).
3. Draw a line segment from centre \(O\) to any point on the boundary as radius \(OA\).
4. Draw a line segment passing through the centre \(O\) connecting two points on the circle as diameter \(AB\).
5. Draw two other line segments connecting two distinct points on the circle's boundary without necessarily passing through the centre as chords \(PQ\) and \(RS\).

In simple words: A circle is a round shape where every point on the edge is the same distance from the centre.

Exam Tip: Always use a sharp pencil and a compass to draw clean circles and label all points clearly with capital letters.

Question 2. Fill in the blanks
a) A ------------- is the line segment that joins any two points on the circle.
b) An -------- is a portion of the circle and is a curved line.
c) In a circle the length of the diameter is always --------------- the length of the radius.
d) The -------------- is the longest chord in a circle.
e) A region bounded by 2 radii and an arc is known as a ------------- of the circle.
Answer:
a) A chord is the line segment that joins any two points on the circle.
b) An arc is a portion of the circle and is a curved line.
c) In a circle the length of the diameter is always twice (or two times) the length of the radius.
d) The diameter is the longest chord in a circle.
e) A region bounded by 2 radii and an arc is known as a sector of the circle.
In simple words: Memorize basic circle vocabulary like chords, arcs, diameters, and sectors to easily solve geometry blanks.

Exam Tip: Remember the core relationship that diameter equals two times the radius (\(d = 2r\)).

Question 3. Name the following with respect to the adjoining figure:
(a) A chord
(b) A diameter
(c) Colour a sector with blue.
(d) Colour a segment with red.
Answer:
(a) A chord: \(PQ\)
(b) A diameter: \(AB\)
(c) Sector: The region enclosed between two radii and arc \(MN\) (shaded or coloured in blue conceptually in the figure between centre and boundary).
(d) Segment: The region enclosed between chord \(PQ\) and arc \(PQ\) (coloured in red conceptually in the figure).

In simple words: A chord connects two points on a circle, while a diameter is a special chord passing through the center.

Exam Tip: Distinguish carefully between a segment (bounded by chord and arc) and a sector (bounded by two radii and an arc).

Question 4. Count and write the number of the triangles in the figure:
Answer:
Let us analyze the complex geometrical figure consisting of vertices \(A, B, C, D, E, F, G, H\):
1. Small triangles at the bottom/middle section: Triangles formed around vertices \(B, C, D, E, F, G, H\).
2. Larger combined triangles including the top vertex \(A\).
Counting systematically, the figure contains a total of 10 triangles.
In simple words: Break down complex intersecting shapes into smaller individual triangles first, then count combinations of adjacent triangles.

Exam Tip: In figures with overlapping lines, list triangles systematically by their vertices to avoid double counting or missing any.

Question 5. Name any three pairs of adjacent angles from the adjoining figure:
Answer:
Adjacent angles share a common vertex and a common arm, and their non-common arms lie on opposite sides of the common arm.
From the given figure with rays and vertices, three pairs of adjacent angles are:
1. Pair 1: \(\angle AOB\) and \(\angle BOC\)
2. Pair 2: \(\angle BOC\) and \(\angle COD\)
3. Pair 3: \(\angle AOC\) and \(\angle COD\)
In simple words: Adjacent angles are angles that are right next to each other, sharing a side and a corner vertex.

Exam Tip: Always check that adjacent angles have the same vertex point and do not overlap in their interiors.