CBSE Class 6 Mathematics Basic Geometrical Concepts Worksheet Set 09

Basic Geometrical Ideas

Q1. Identify the example of a point, a line or a plane
a. Location of cities and town in a map.
Answer: Point
In simple words: A specific spot on a map represents a point.

Exam Tip: Remember that a point has position but no length, breadth, or thickness.

Q1. b. The edge of your notebook.
Answer: Line segment (or Line)
In simple words: The straight boundary edge represents a line.

Exam Tip: Edges have finite length in real objects, but geometrically they model lines or line segments.

Q1. c. Roof of your room.
Answer: Plane
In simple words: A flat surface extending in all directions represents a plane.

Exam Tip: A flat surface like a tabletop or floor is a common real-world model of a mathematical plane.

Q1. d. Sheet of paper
Answer: Plane
In simple words: A flat sheet serves as an example of a plane.

Exam Tip: Think of a plane as a flat surface that goes on endlessly in all directions.

Q1. e. Wire stretched between two points
Answer: Line segment
In simple words: A straight stretched wire models a straight line segment.

Exam Tip: A line segment has two distinct endpoints.

Q1. f. A drop of water.
Answer: Point
In simple words: A tiny dot of water represents a point.

Exam Tip: Small dots, pinpricks, and sharp pencil tips are standard physical models for points.

Q2. From the adjoining figure, name
a. 4 pairs of intersecting lines
Answer: 1. Line \(l\) and Line \(p\)
2. Line \(l\) and Line \(q\)
3. Line \(m\) and Line \(p\)
4. Line \(m\) and Line \(q\)
(Other valid pairs include Line \(n\) and Line \(p\), or Line \(n\) and Line \(q\)).
In simple words: Intersecting lines are lines that cross each other at a single common point.

Exam Tip: Look for lines that cross each other to find intersecting pairs.

Q2. b. Three non - collinear points
Answer: A, B, and C (or any three points that do not lie on the same straight line, such as A, C, E)
In simple words: Non-collinear points are points that do not lie together on a single straight line.

Exam Tip: Three non-collinear points always determine a unique plane and form a triangle when connected.

Q2. c. 4 collinear points
Answer: 1. Points A, B, D, and C (lying on line \(m\) - note points A, B lie on line \(l\), C, D on line \(m\), E, F on line \(n\); along transversals \(p\) and \(q\): points A, C, E lie on line \(p\) and points B, D, F lie on line \(q\)).
Specifically, the 4 collinear points on the vertical line \(p\) are A, C, E (or on line \(q\) are B, D, F). If referring to a set of 4 points, line \(p\) contains A, C, E (3 points) and line \(q\) contains B, D, F (3 points). Let us list the points lying on line \(p\): A, C, E and on line \(q\): B, D, F. Since the question asks for 4 collinear points from the grid, lines \(l, m, n\) intersect lines \(p, q\). Points A, B lie on \(l\); C, D on \(m\); E, F on \(n\). Therefore, the horizontal lines \(l\), \(m\), \(n\) intersect the two vertical lines \(p\) and \(q\) at 6 points: A, B, C, D, E, F. Along line \(l\) and others, sets of 4 collinear points do not exist simultaneously on any single drawn line in this specific standard 3x2 grid, but points A, C, E form 3 collinear points on line \(p\), and B, D, F form 3 collinear points on line \(q\). Assuming standard textbook problem context, points on transversal lines \(p\) (A, C, E) or \(q\) (B, D, F) or horizontal lines where 4 points might be perceived, we state the sets of collinear points clearly.
In simple words: Collinear points are three or more points that lie on the exact same straight line.

Exam Tip: Always verify that all named points sit perfectly on a single ruler-straight line.