Geometry
Geometry

This free course is available to start right now. Review the full course description and key learning outcomes and create an account and enrol if you want a free statement of participation.

Free course

Geometry

2 Shapes and symmetry

2.1 Geometric shapes – triangles

This section deals with the simplest geometric shapes and their symmetries. All of the shapes are two-dimensional – hence they can be drawn accurately on paper.

Simple geometric shapes are studied in mathematics partly because they are used in thousands of practical applications. For instance, triangles occur in bridges, pylons and, more mundanely, in folding chairs; rectangles occur in windows, cinema screens and sheets of paper; while circles are an essential part of wheels, gears and plates.

By definition, triangles are shapes with three straight sides. However, there are various types of triangle:

An equilateral triangle is a triangle with all three sides of equal length. The three angles are also all equal.

An isosceles triangle is a triangle with two sides of equal length. The two angles opposite the equal sides are also equal to one another.

A right-angled triangle is a triangle with one angle that is a right angle.

A scalene triangle is a triangle with all the sides of different lengths. The angles are also all different.

It is a general convention that equal sides are marked by drawing a short line, /, through them, and a right angle is marked by a square between the arms of the angle. If sides and angles are not marked, do not assume that they are equal, just because they look equal!

Activity 6: Special triangles

Click here [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] for Activity 6.

MU120_4M7

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has over 40 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to university level study, find out more about the types of qualifications we offer, including our entry level Access courses and Certificates.

Not ready for University study then browse over 900 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus