The primary sector involves activities that:

produce goods directly from nature

Which of these belongs to the secondary sector?

Manufacturing cloth from cotton in a factory

What shape is formed by all points at a fixed distance from a point \(P\)?

A circle, with \(P\) as its centre and the fixed distance as its radius.

What is the radius of a circle?

The distance between the centre of the circle and any point on the circle.

What two properties define a rectangle?

Its opposite sides are equal in length (R1) and all four of its angles are \(90^\circ\) (R2).

What extra property makes a square different from a rectangle?

A square has all four sides equal, in addition to all angles being \(90^\circ\).

Does rotating a square change whether it is a square?

No; rotation does not change side lengths or angles, so a rotated square is still a square.

How can a rectangle be validly named?

By listing its corners in the order you travel around it, starting from any corner, e.g. ABCD or BCDA.

Which instrument helps draw a perpendicular and transfer equal lengths in constructions?

A compass, together with a ruler, is used to draw arcs, transfer lengths and locate points.

When does a diagonal divide a rectangle\u2019s corner angles into two equal parts?

Only when the rectangle is a square (all four sides equal).

How are the two diagonals of a rectangle related in length?

The two diagonals of a rectangle are equal in length.

Is there a four-sided figure with all sides equal that is not a square?

Yes; a rhombus has all sides equal but its angles need not be \(90^\circ\), so it is not a square.

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Chapter 8: Playing with Constructions — Class 6 Mathematics

Mathematics · 10 chapters

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Chapter 8: Playing with Constructions

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All the points at a fixed distance from a point \(P\) form a

Summary

This chapter introduces geometric construction using a ruler and a compass. Starting from freehand artwork, students discover that all points at a fixed distance from a point \(P\) form a circle, where \(P\) is the centre and the fixed distance is the radius. The compass is used to draw circles and arcs of given radius. The chapter then revisits squares and rectangles and their defining properties: a rectangle has opposite sides equal and all angles \(90^\circ\) (R1 and R2), while a square additionally has all four sides equal (S1 and S2). Rotating a square or rectangle does not change these properties. Students construct squares and rectangles of given side lengths by drawing perpendiculars and transferring lengths with a compass, and learn to name figures by going around their corners in order. They construct rectangles from a side and a diagonal, and rectangles whose diagonals divide the corner angles into given parts, discovering that equal division happens only for a square. The diagonals of a rectangle are shown to be equal, and the chapter closes with locating points equidistant from two given points (used to build figures like a house) and constructing four-sided figures with all sides equal.

Artwork with Ruler and CompassCircle, Centre and RadiusSquares and Rectangles and their PropertiesConstructing Squares and RectanglesDiagonals of Rectangles and SquaresPoints Equidistant from Two Points

Key terms

Circle

The set of all points at a fixed distance from a centre point.

Radius

The fixed distance between the centre of a circle and any point on the circle.

Compass

A geometry instrument used to draw circles and arcs of a chosen radius.

Rectangle properties

A rectangle has opposite sides equal (R1) and all angles \(90^\circ\) (R2).

Square properties

A square has all sides equal (S1) and all angles \(90^\circ\) (S2).

Diagonal

A line segment joining two opposite corners of a rectangle or square.

Important questions

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Which of the following is not a name for this square?

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Circle

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The set of all points at a fixed distance from a centre point.

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