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CBSE Notes Class 6 Maths Chapter 8 Playing with Constructions
Chapter 8 of the CBSE Class 6 Maths, 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.
Introduction 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.
Drawing a Line Segment
Definition: A line segment is a part of a line with two endpoints.
Steps:
- Place the ruler on the paper.
- Mark two points, say A and B, at the required distance.
- Draw a straight line between A and B.
Constructing a Circle
Key Elements of a Circle:
- Radius: Distance from the centre to any point on the circle.
- Diameter: Twice the radius.
- Center: The fixed point inside the circle.
Steps:
- Place the compass point on the centre.
- Adjust the compass to the required radius.
- Rotate the compass to draw the circle.
Perpendicular Lines
Definition: Two lines are perpendicular if they meet at a right angle (90°).
Construction Steps:
- Draw a line segment AB.
- Place the protractor on the given line segment with its centre at the point where the perpendicular is to be drawn.
- Mark the 90° angle using the protractor.
- 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.
Squares 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.
Constructing 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.
Points 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:
- Draw a line segment AB.
- Place the compass point on A and draw an arc above and below AB.
- Repeat with the compass point on B.
- Connect the intersection points of the arcs to bisect the line segment.
Practical Applications of Constructions
- Creating floor plans.
- Designing patterns in art and crafts.
- Understanding real-life objects like bridges and wheels.
1.0Important 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.
2.0Practice Questions
- Draw a line segment of 7 cm and bisect it.
- Construct a circle with a radius of 4.5 cm.
- Using a protractor, draw an angle of 120°.
- Draw perpendicular lines to a given line segment.
- Identify and name the types of angles in the given figure.
Key Concepts to Remember
- Using a ruler and compass: A ruler helps draw straight lines, while a compass is used to draw circles and arcs. Both tools help us make accurate geometric figures.
- Circles and their centre: A circle is made up of points that are all at the same distance from a fixed point. This fixed point is called the centre.
- Radius of a circle: The radius is the distance from the centre to any point on the circle. For example, if a circle has a radius of 4 cm, every point on its boundary is 4 cm from the centre.
- Drawing circles and arcs: A compass can draw a complete circle or just a part of one, called an arc. Keeping the compass opening unchanged helps us draw arcs of the same radius.
- Properties of a rectangle: A rectangle has four right angles, each measuring 90°. Its opposite sides are equal.
- Properties of a square: A square has four equal sides and four right angles. It also has all the properties of a rectangle.
- Naming squares and rectangles: We name a square or rectangle by following its corners in order. For example, rectangle ABCD can also be called BCDA, CDAB or DABC.
- Rotated squares and rectangles: A square or rectangle remains the same shape even when it is tilted or turned. Its side lengths and angles do not change.
- Constructing squares: Start by drawing one side of the required length. Draw perpendicular lines at its endpoints, mark equal lengths on them, and join the remaining endpoints.
- Constructing rectangles: Draw the given side and construct perpendicular lines at its endpoints. Mark the required lengths and join the points to complete the rectangle.
- Points on the sides of a rectangle: Moving points along the sides of a rectangle changes their positions and may change the distance between them. Drawing and measuring the joining line segment helps us explore this relationship.
- Dividing rectangles into squares: Some rectangles can be divided into two or more equal squares. A rough sketch can help you work out the dimensions before making the final construction.
- Diagonals of squares and rectangles: A diagonal joins two opposite corners of a shape. Drawing the diagonals helps us compare their lengths and see how they cross each other.
- Constructing a rectangle using a diagonal: If one side and the diagonal are given, a ruler, compass and perpendicular lines can help locate the missing corner.
- Finding points at equal distances: A point that is equally distant from two given points can be found using arcs drawn with a compass. The intersection of arcs with equal radii gives a point at the required distance from both centres.
- Planning a construction: Before starting, make a rough sketch and note the given measurements. This makes it easier to decide which lines, arcs and perpendiculars to draw first.
3.0Important Formulas – Playing with Constructions
This chapter is mainly about drawing geometric figures rather than learning numerical formulas. The following properties and rules will help you complete the constructions correctly.
Constructing a Square with a Given Side
Let us construct a square PQRS with each side measuring 6 cm.
- Draw a line segment PQ = 6 cm.
- Draw a perpendicular to PQ at P.
- Mark S on the perpendicular so that PS = 6 cm.
- Draw a perpendicular to PQ at Q.
- Mark R on this perpendicular so that QR = 6 cm, on the same side of PQ as S.
- Join R and S to complete the square PQRS.
Check that all four sides are equal and each angle measures 90°.
Constructing a Rectangle with Given Side Lengths
Let us draw a rectangle ABCD with sides of 6 cm and 4 cm.
- Draw AB = 6 cm.
- Draw perpendicular lines to AB at A and B.
- Mark AD = 4 cm and BC = 4 cm on the same side of AB.
- Join C and D to complete the rectangle ABCD.
Check that AB = CD, AD = BC, and all four angles are 90°.
Constructing a Rectangle Using One Side and a Diagonal
Suppose a rectangle has one side of 5 cm and a diagonal of 7 cm.
- Draw DC = 5 cm.
- Draw a perpendicular to DC at C.
- Open the compass to 7 cm and, with D as the centre, draw an arc that cuts the perpendicular at B.
- Draw a perpendicular to DC at D.
- Draw a perpendicular to BC at B. Let the perpendiculars from D and B meet at A.
- Join AB and AD to complete rectangle ABCD.
Check that the angles are right angles, the opposite sides are equal, and DB = 7 cm.
Finding Points Equidistant from Two Given Points
Suppose you need to find a point A that is 5 cm from both B and C.
- Draw an arc with B as the centre and a radius of 5 cm.
- Draw another arc with C as the centre and the same radius.
- Mark an intersection of the arcs as A.
- Join A to B and A to C.
Since both arcs have a radius of 5 cm, AB = AC = 5 cm. Therefore, A is equally distant from B and C.
4.0Learning Guide for Class 6 Maths Playing with Constructions – Chapter 8
- Practising with a compass: Mark a point P on paper and set your compass to 4 cm using a ruler. Keep the pointed end at P and turn the compass to draw a circle. Every point on the circle will be 4 cm from P.
- Drawing circles and arcs: Draw circles with different radii. Then try drawing only a part of a circle to practise making arcs.
- Making simple drawings with a compass: Try drawing simple patterns, wavy lines or pairs of circles using a ruler and compass. Changing the compass opening and the position of its point will help you create different shapes.
- Identifying squares and rectangles: Draw both shapes and measure their sides and angles. Check that opposite sides of a rectangle are equal and that all four sides of a square are equal.
- Recognising rotated shapes: Turn your paper after drawing a square or rectangle. Notice that the shape remains the same even when it is tilted.
- Constructing a square: Draw a square with a side of 6 cm using a ruler and compass. Measure its sides and angles to check whether your construction is correct.
- Drawing rectangles of different sizes: Construct rectangles measuring 4 cm by 6 cm and 2 cm by 10 cm. Compare their dimensions and check whether both follow the properties of a rectangle.
- Exploring points on rectangle sides: Draw rectangle ABCD and mark points X and Y on opposite sides. Move the points to different positions and measure XY. Observe how the distance changes.
- Dividing a rectangle into squares: Draw a rectangle that can be divided into two equal squares. Then try dividing another rectangle into three equal squares. Plan the dimensions before drawing the final figures.
- Drawing a square inside a rectangle: Draw a rectangle measuring 8 cm by 4 cm. Try placing a square inside it so that both shapes have the same centre. Use a rough sketch to plan where the corners should lie.
- Exploring diagonals: Draw rectangle PQRS and join P to R and Q to S. Measure both diagonals and compare their lengths. Repeat the activity with a square and note what you observe.
- Constructing a rectangle using a diagonal: Draw a rectangle with one side measuring 5 cm and a diagonal measuring 7 cm. Use a compass and perpendicular lines to locate the missing corner.
- Making a geometric house: Try drawing a house-shaped figure using a ruler and compass. Use arcs to locate points at the required distances, then join the points to complete the shape.
- Checking your construction: Measure the sides and angles after completing a figure. If something does not match the given measurements, check the compass opening and the positions of the perpendicular lines.
5.0Explore Chapter-wise Class 6 Maths Notes
6.0Additional Study Materials for Class 6 Maths
7.0Find the Right Study Resources for Class 6
8.0Benefits of CBSE Notes for Class 6 Maths Chapter 8 - Playing with Constructions
- Enhanced Accuracy in Constructions: Following well-structured CBSE Notes helps students perform constructions precisely, leading to correct geometric figures.
- Time-Saving Resource: The CBSE Notes for Class 6 condense the essential information, saving students the time of sifting through lengthy textbook chapters.
- Building a Strong Foundation: Mastering the concepts in this chapter lays a crucial foundation for more advanced geometry topics in higher classes.
- Self-Paced Learning: Students can refer to the notes at their own pace, revisiting concepts they find challenging.
- Preparation for Assessments: The notes often include important definitions, properties, and example problems that are likely to appear in school assessments.