Class 6 ยท Maths ยท Ganita Prakash
Chapter 8 ๐งญ
Chapter 8 ๐งญ
Playing with Constructions
Quick, colourful revision notes โ easy to read before your test!
Chapter Contents
8.1 Circles & the Compass
A curve is any shape drawn on paper โ including straight lines, circles, and more. A compass is the tool used to draw circles and arcs of a fixed radius.
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Fig 1: Every point exactly 4 cm from P traces out a perfect circle
A circle is simply the set of all points at a fixed distance (the radius) from a fixed centre point.
8.2 Squares & Rectangles
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Fig 2: Properties that define a rectangle and a square
Rectangle: opposite sides equal + all angles 90ยฐ.
Square: all sides equal + all angles 90ยฐ (a special rectangle!).
Square: all sides equal + all angles 90ยฐ (a special rectangle!).
A valid name for a shape must list corners in order around the boundary (e.g. ABCD, BCDA, DCBA โ but NOT ACBD). Rotating a square/rectangle doesn't change its properties โ it's still a square/rectangle!
8.3 Constructing Squares & Rectangles
To construct a square of side 6 cm: draw side PQ = 6 cm โ draw a perpendicular at P (and at Q) using a compass or protractor โ mark 6 cm along each perpendicular to get S and R โ join RS to complete the square.
Can a 4-sided figure have all angles = 90ยฐ but opposite sides not equal? No โ if all angles are 90ยฐ, it must be a rectangle, which forces opposite sides to be equal!
8.5 Diagonals of Rectangles & Squares
In a rectangle, both diagonals are equal in length, and they bisect each other (cross at their midpoints).
In a square specifically, the diagonals are also equal in length and cross at exactly 90ยฐ, and each diagonal splits its corner angle into two equal 45ยฐ angles.
In a square specifically, the diagonals are also equal in length and cross at exactly 90ยฐ, and each diagonal splits its corner angle into two equal 45ยฐ angles.
8.6 Points Equidistant from Two Given Points
How do we find a point exactly the same distance from two fixed points B and C โ without trial and error?
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Fig 3: Draw equal-radius circles centred at B and C โ they cross at 2 points, both equidistant from B and C
The line joining these two crossing points is the perpendicular bisector โ it cuts BC exactly in half, at a right angle!
๐ฏ Quick Summary
- A circle = all points at a fixed distance (radius) from a centre โ drawn using a compass.
- Rectangle: opposite sides equal, all angles 90ยฐ. Square: all sides equal, all angles 90ยฐ.
- Rotating a shape doesn't change whether it's a square/rectangle.
- Rectangles/squares are constructed using perpendiculars and equal side lengths.
- Diagonals of a rectangle are equal & bisect each other; a square's diagonals also cross at 90ยฐ and bisect the corner angles.
- Two circles of equal radius from two points cross at points equidistant from both โ this locates the perpendicular bisector.
โ๏ธ Notes by @edugrown โ happy revising! ๐