Teaching mathematics
Teaching mathematics

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Teaching mathematics

3.2 Angle sum of triangles

The angles of any triangle sum to 180⁰. This can be proved in several ways and can easily be shown to convince learners as a classroom activity.

Activity 5 Demonstrating the angle sum of a triangle

Timing: Allow 15 minutes

You will need paper, pen, ruler and scissors.

Draw any triangle and mark the angles at the corners.

Cut out the triangle.

Tear off the corners then put the corner angles together. They should all form a straight line.

If we accept that there are 360⁰ in a circle and 180⁰ on a straight line then we have shown that the three corners add up to 180⁰.

Discussion

This activity can be done in the classroom. If 30 learners can do this activity using 30 different triangles then they will have demonstrated the angle sum of a triangle in 30 different ways. This is not a proof, merely a demonstration that it works.

It is much more fun for learners if they discover angle facts for themselves, rather than being simply told them.

Think of other ways for learners to discover the angle facts using drawing and cutting, and measuring using a protractor.

Simple angle facts
Figure 10 Simple angle facts

Activity 6 A problem using angle facts

Timing: Allow 15 minutes

Below is a design using 8 congruent (i.e. exactly the same size and shape) rhombuses. Calculate the two different angles in the rhombuses.

Design created using eight rhombuses
Figure 11 Design created using eight rhombuses

Discussion

Think about the number of rhombuses which meet in the middle of the design. Their sum must be 360⁰.

Think about the rhombus as a quadrilateral. Its angles must sum to 360⁰. A rhombus has two pairs of equal angles.

Use compasses and a protractor to recreate this design. Begin by drawing a circle and marking off 8 equally spaced points on the circumference. Use these points to draw the bottom halves of the 8 rhombuses.

To find the top points for each rhombus use the compasses opened to the same radius as when you drew the circle. Draw 2 arcs (parts of circles) from each point which will intersect in pairs above the rhombus halves. These intersections are the top points of the rhombuses. Join these to the circumference to complete the rhombuses.

TM_1

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 50 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, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 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 prospectus371