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In this chapter, you will learn how to construct, or draw, different lines, angles and shapes. You will use drawing instruments, such as a ruler, to draw straight lines, a protractor to measure and draw angles, and a compass to draw arcs that are a certain distance from a point. Through the various constructions, you will investigate some of the properties of triangles and quadrilaterals; in other words, you will find out more about what is always true about all or certain types of triangles and quadrilaterals. Bisecting linesWhen we construct, or draw, geometric figures, we often need to bisect lines or angles.Bisect means to cut something into two equal parts. There are different ways to bisect a line segment.
CD is called a bisector because it bisects AB. AF = FB.
In Grade 6, you learnt how to use a compass to draw circles, and parts of circles called arcs. We can use arcs to bisect a line segment.
Notice that CD is also perpendicular to AB. So it is also called a perpendicular bisector.
Constructing perpendicular lines
Bisecting anglesAngles are formed when any two lines meet. We use degrees (°) to measure angles. In the figures below, each angle has a number from 1 to 9.
Constructing special angles without a protractor
Challenge Work in your exercise book. Try to construct the following angles without using a protractor: 150°, 210° and 135°. Constructing trianglesIn this section, you will learn how to construct triangles. You will need a pencil, a protractor, a ruler and a compass. A triangle has three sides and three angles. We can construct a triangle when we know some of its measurements, that is, its sides, its angles, or some of its sides and angles. Constructing triangles when three sides are given
Constructing triangles when certain angles and sides are given
If triangles are exactly the same, we say they are congruent.
Challenge
Properties of trianglesThe angles of a triangle can be the same size or different sizes. The sides of a triangle can be the same length or different lengths.
We can conclude that the interior angles of a triangle always add up to 180°. Properties of quadrilateralsA quadrilateral is any closed shape with four straight sides. We classify quadrilaterals according to their sides and angles. We note which sides are parallel, perpendicular or equal. We also note which angles are equal.
We can conclude that the interior angles of a quadrilateral always add up to 360°. Constructing quadrilateralsYou learnt how to construct perpendicular lines in section 10.2. If you know how to construct parallel lines, you should be able to construct any quadrilateral accurately.
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