Chapter 8: Playing with Constructions
With only a ruler, a compass and a sharp pencil you can draw circles, waves, flowers, perfect rectangles and squares. In this chapter we draw artwork with circles, learn what makes a rectangle or a square, construct them step by step, explore their diagonals, and use circles to find points that are the same distance from two places.
In this chapter you will
- draw circles and arcs with a compass and make patterns
- know the properties of rectangles and squares
- construct rectangles and squares from given measurements
- find points equidistant from two points using circles
Topics
- Artwork NCERT 8.1
All points of a circle are the same distance (the radius) from its centre.
- Squares and Rectangles NCERT 8.2
Rectangle: opposite sides equal, all angles 90°.
- Constructing Squares and Rectangles NCERT 8.3
A rough sketch helps plan a construction.
- An Exploration in Rectangles NCERT 8.4
XY is shortest (equal to AB) when X and Y are the same distance from A and B.
- Diagonals of Rectangles and Squares NCERT 8.5
The diagonals of a rectangle are equal and cut each other in half.
- Points Equidistant from Two Points NCERT 8.6
Points at the same distance from B and from C: draw equal circles (or arcs) around both; they meet at those points.
Key words
- Circle
- all the points at the same distance from a centre
- Radius
- the distance from the centre to the circle
- Arc
- a part of a circle
- Compass
- a tool for drawing circles and copying lengths
- Diagonal
- a line joining opposite corners
- Equidistant
- at the same distance
Summary
- All points of a circle are the same distance, the radius, from its centre.
- A compass draws circles and arcs and copies lengths exactly.
- A rough sketch helps plan a construction.
- A rectangle can be constructed from its two sides, or from one side and a diagonal.
- The diagonals of a rectangle are equal and cut each other in half; in a square they also cross at 90°.