Class 6 — Mathematics (NCERT)
Basic Geometrical Ideas
Class 6
- ✓By the end of this lesson students will be able to define and identify basic geometrical terms like point, line segment, line, and ray.
- ✓By the end of this lesson students will be able to differentiate between intersecting and parallel lines.
- ✓By the end of this lesson students will be able to define an angle and identify its vertex and arms.
- ✓By the end of this lesson students will be able to recognise and classify different types of polygons based on their number of sides.
- ✓By the end of this lesson students will be able to identify and label various parts of a circle, including its centre, radius, diameter, chord, and arc.
Key concepts
A point is a mark of position. It has no length, breadth, or height. It is represented by a tiny dot and is usually denoted by a capital letter. For example, Point A, Point P.
A line segment is a part of a line that has two distinct endpoints. It has a definite length. We denote a line segment joining points A and B as AB or BA.
A line is a straight path that extends indefinitely in both directions without any endpoints. It has no definite length. We denote a line passing through points A and B as AB or by a single lowercase letter, for example, line 'l'.
A ray is a part of a line that has one endpoint and extends indefinitely in one direction. We denote a ray starting at point A and passing through point B as AB. The endpoint is always written first.
Two lines are called intersecting lines if they meet at a common point. This common point is called the point of intersection.
Two lines are called parallel lines if they never meet, no matter how far they are extended in either direction. The perpendicular distance between parallel lines always remains the same.
An angle is formed when two rays share a common endpoint. The common endpoint is called the vertex, and the two rays are called the arms or sides of the angle. An angle is denoted by the symbol '∠'. For example, ∠ABC or ∠B.
A polygon is a simple closed figure made up of three or more line segments. These line segments are called the sides of the polygon, and the points where the sides meet are called vertices. Examples include triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), and hexagons (6 sides).
A circle is a simple closed curve, all points of which are at the same fixed distance from a fixed point inside it. This fixed point is called the centre of the circle.
1. Centre: The fixed point inside the circle from which all points on the circle are equidistant.\n2. Radius: A line segment connecting the centre to any point on the circle.\n3. Diameter: A chord that passes through the centre of the circle. It is the longest chord and is twice the length of the radius (Diameter = 2 × Radius).\n4. Chord: A line segment joining any two points on the circle.\n5. Arc: A portion or part of the circumference of a circle.\n6. Circumference: The distance around the circle, i.e., its perimeter.\n7. Interior: The region inside the circle.\n8. Exterior: The region outside the circle.
Key facts to remember
- 1A point indicates a position and has no dimension.
- 2A line segment has two endpoints and a definite length.
- 3A line extends infinitely in both directions and has no endpoints.
- 4A ray has one endpoint and extends infinitely in one direction.
- 5Parallel lines never intersect, while intersecting lines meet at a single point.
- 6An angle is formed by two rays sharing a common endpoint (vertex).
- 7Polygons are closed figures made up of three or more line segments.
- 8A circle is a set of all points equidistant from a central point.
- 9The diameter of a circle is its longest chord and is twice the length of its radius.
Worked examples
Example 1
Observe the given figure description and identify:\n(a) a line\n(b) two rays\n(c) two line segments\n(d) a point\n\nFigure Description: A straight line 'l' passes through points P, Q, R in that order. From point Q, a ray QS extends upwards. From point R, a ray RT extends downwards.
Answer
(a) A line: Line PR (or Line l)\n(b) Two rays: Ray QS, Ray RT (Other valid options include Ray QP, Ray QR)\n(c) Two line segments: Line segment PQ, Line segment QR (Other valid option includes Line segment PR)\n(d) A point: P (Other valid options include Q, R, S, T)
Remember the correct notation for each figure: AB for line segment, AB for line, and AB for ray (where A is the endpoint).
Example 2
Draw a circle and label its:\n(a) centre\n(b) a radius\n(c) a diameter\n(d) a chord\n(e) an arc
Answer
A correctly drawn circle with the following labels:\n(a) Centre: O\n(b) Radius: OA\n(c) Diameter: BC\n(d) Chord: DE\n(e) Arc: FG
Ensure your labels are clear and correspond to the correct parts of the circle.
Example 3
Which of the following figures are polygons?\n(a) A figure with 4 straight sides forming a closed shape.\n(b) A figure with 3 straight sides forming a closed shape.\n(c) A figure with a curved boundary forming a closed shape.\n(d) A figure with 5 straight sides but not closed.
Answer
Figures (a) and (b) are polygons.
Remember, a polygon must be both 'closed' and made entirely of 'straight line segments'.
Common mistakes
- ✗Confusing the notation for a line (AB), line segment (AB), and ray (AB).
- ✗Incorrectly identifying the vertex and arms of an angle.
- ✗Thinking that a circle or any figure with curved sides is a polygon.
- ✗Not understanding that a diameter is a special type of chord that passes through the centre.
- ✗Drawing open figures when asked to draw polygons, which must always be closed.
Exam tips
- ★Pay close attention to the specific notation (e.g., AB vs. AB vs. AB) when identifying or drawing lines, line segments, and rays.
- ★Clearly label all parts of diagrams as requested in the question to avoid losing marks.
- ★Memorise the precise definitions of key terms like radius, diameter, chord, and arc for circles, and sides/vertices for polygons.
- ★Practice drawing different geometric figures accurately using a ruler and compass where appropriate.
Ready to practise?
Try a problem on this topic
Snap a photo or type a question — get step-by-step working instantly.