Topics covered within this unit: 15.1 Introduction 15.2 Introduction to triangles
15.3 Constructing triangles using angles and sides
15.4 Types of triangles and area of triangles 15.5 Right-angled triangles 15.6 Interior and exterior angles in triangles
The Learning Outcomes covered in this unit are contained in the following sections:
GT.1 GT.2a GT.2c GT.3a GT.3b
Key words Polygon
Quadrilateral Triangle Isosceles triangle Scalene triangle Equilateral triangle Included angle Included side Right-angled triangle Hypotenuse Exterior angle Interior angle
Polygons
Something to think about …
A right angle is equal to 90°.
It has been suggested that the technique for the construction of a ‘right angle by stretched rope’, may have been used by the ancient Egyptians to survey their fi elds.
This technique involved a rope knotted at regular intervals, so that there are 12 equal segments.
Using this ‘rope’, sketch a 2D shape with: ● ● ● ●
● ●
four sides and with two pairs of sides with diff erent lengths four sides and four equal sides
three sides which are all equal in length
three sides where only two sides are equal in length three sides where no two sides are equal in length three sides and with one 90 ° internal angle
15·1 Introduction
By the end of this section you should: ● understand the terms: polygon, quadrilateral, rectangle and square ● understand the principle of area and the principle of perimeter ● be able to construct a rectangle
Polygons A polygon is any two-dimensional shape formed with straight lines.
Polygons are many-sided fi gures, with sides that are line segments. Polygons are named according to the number of sides and angles they have. We have already met some polygons, but now we will examine them in more detail.
Triangle Square
Side: any line segment which makes up the polygon.
Vertex: the end points where two sides meet (plural is vertices).
Adjacent sides: sides that meet. Rectangle Hexagon Vertex Side