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. Show
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. Bisecting a line segment with a ruler
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. Bisecting a line segment with a compass and ruler
Notice that CD is also perpendicular to AB. So it is also called a perpendicular bisector.
Constructing perpendicular linesA perpendicular line from a given point
A perpendicular line at a given point on a line
Bisecting anglesAngles are formed when any two lines meet. We use degrees (°) to measure angles. Measuring and classifying anglesIn the figures below, each angle has a number from 1 to 9.
Bisecting angles without a protractor
Constructing special angles without a protractorConstructing angles of and
Constructing angles of and
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 trianglesConstructing 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. Properties of equilateral triangles
Properties of isosceles triangles
The sum of the angles in a triangle
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. Properties of quadrilaterals
Sum of the angles in a quadrilateral
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. Constructing parallel lines to draw quadrilaterals
What is the easiest way to find angles?The easiest way to measure an angle is to use a protractor. However, if you don't have a protractor handy, you can determine the size of an angle using the basic geometric principles of triangles. You'll need a scientific calculator to solve the equations.
What are the 3 ways to measure angles?There are three units of measure for angles: revolutions, degrees, and radians.
How do you find a 45 degree angle without a protractor?Explanation:. Draw a line segment BC of any length.. Taking B as the center, construct a semicircle that bisects BC at point P.. From P, construct three arcs dividing the semi-circle into 3 equal parts that are 60º each.. Mark the points as x and y where the arcs bisect the semi-circle.. |