CBSE Notes Class 6 Maths Chapter 8 Playing with Constructions

Chapter 8 of the CBSE Class 6 Mathematics syllabus, Playing with Constructions, introduces students to basic geometric constructions. It builds a strong foundation for understanding shapes, measurements, and the tools needed for precise constructions. 

1.0Introduction to Construction Tools

• Ruler: Used to measure and draw straight lines.
• Compass: Helps in drawing circles and arcs of specific radii.
• Divider: Used for comparing lengths.
• Set Squares: Tools for drawing perpendicular and parallel lines.
• Protractor: Measures angles in degrees.

2.0Drawing a Line Segment

Definition: A line segment is a part of a line with two endpoints.

Steps:

1. Place the ruler on the paper.
2. Mark two points, say A and B, at the required distance.
3. Draw a straight line between A and B.

3.0Constructing a Circle

Key Elements of a Circle:

4. Radius: Distance from the center to any point on the circle.
5. Diameter: Twice the radius.
6. Center: The fixed point inside the circle.

Steps:

1. Place the compass point on the center.
2. Adjust the compass to the required radius.
3. Rotate the compass to draw the circle. 

4.0Perpendicular Lines

Definition: Two lines are perpendicular if they meet at a right angle (90°).

Construction Steps:

1. Draw a line segment AB.
2. Place the protractor on the given line segment with its center at the point where the perpendicular is to be drawn.
3. Mark the 90° angle using the protractor.
4. Remove the protractor and use a scale to draw a straight line passing through the marked point. This line will be perpendicular to the original segment.

5.0Squares and Rectangles

Properties of Squares:

• All four sides are equal.
• Opposite sides are parallel.
• Diagonals bisect each other at right angles and are equal in length.

Properties of Rectangles:

• Opposite sides are equal and parallel.
• All angles are right angles (90°).
• Diagonals are equal in length and bisect each other.

6.0Constructing Squares and Rectangles

Steps to Construct a Square:

• Draw a line segment of the desired side length.
• Use a compass to construct perpendiculars at each endpoint.
• Mark the same side length on these perpendiculars and connect the points to form the square.

Steps to Construct a Rectangle:

• Draw one side of the rectangle.
• Construct perpendiculars at the endpoints using a protractor or set square.
• Mark the required length for the opposite side and join the points to form the rectangle.

7.0Points Equidistant from Two Given Points

The concept of a perpendicular bisector is introduced as the set of points equidistant from two fixed points.

Steps to Construct a Perpendicular Bisector:

1. Draw a line segment AB.
2. Place the compass point on A and draw an arc above and below AB.
3. Repeat with the compass point on B.
4. Connect the intersection points of the arcs to bisect the line segment.

8.0Practical Applications of Constructions

• Creating floor plans.
• Designing patterns in art and crafts.
• Understanding real-life objects like bridges and wheels.

9.0Important Tips for Students

• Practice using geometric tools to become familiar with their handling.
• Follow the steps of construction accurately to avoid errors.
• Verify your construction by measuring with a ruler or protractor.

10.0Practice Questions

1. Draw a line segment of 7 cm and bisect it.
2. Construct a circle with a radius of 4.5 cm.
3. Using a protractor, draw an angle of 120°.
4. Draw perpendicular lines to a given line segment.
5. Identify and name the types of angles in the given figure.