From Angles to Triangles

WARM UP

Create different, clear geometric shapes by standing still like statues. Create statues at floor level (on the ground), at intermediate level (sitting or kneeling), and at a higher level (standing). You can also create shapes together.

What kind of different triangles can you create with your own body? Can you make a really small triangle? Or a really big one? With what different parts of the body can you create a triangle? What if you create triangles with one or two classmates?

Stand in a large room so that everyone has their own space around them. Each student must choose two other students, who can be their secret triangle friends. No one should reveal which students they have chosen. When the music starts playing, everyone is allowed to move freely in the room, but you must make sure that you are always at an equal distance from both your triangle friends.

Divide into groups of three. Each group stands inside a ring created by a long rubber band. Each group should create a triangle using their rubber band. The groups are allowed to move freely to the beat of music. How does the triangle change when the tips move? Try different levels and poses. The rubber band can be held at the waist, ankles, wrists.

Stretch out both arms in front of you. Then a smaller or larger angle is formed between the arms. If you are in a room where the corners consist of 90-degree angles, you can stand in a corner and try how it feels on your arms to form an angle of 90 degrees. What does the angle between the arms look like if it has less or more than 90 degrees?
Divide the room in half with a line. One half is too blunt angles, the other too acute angles. The arm angles are allowed to move freely on both sides of the centerline, but when they hit the centerline, they should stop and stiffen to 90-degree angles. You get away from the center line when another angle hits the center line, so that the angles together amount to 180 degrees. After that, both angles are allowed to continue their journey in any half of the room.
Feel free to use some type of background music in the assignment!

The task is a continuation of the previous task with different angles in the room. When the music stops, all the students should stop moving and keep the angle they have between their arms unchanged. Then the students should seek out two other students and try to form a triangle with them.
What do you notice? Can all groups form a triangle? You notice quite quickly that any three angles cannot form a triangle together.

Demonstrate physically that the sum of a triangle’s angles is 180 degrees.
A student should stand at the centre line and form a 180-degree angle with their arms. Another student stands next to them, and the first student reduces their own angle, so that the sum of the two new angles is 180 degrees. A third student stands between the first two, and now both first two angles need to be smaller for the third to be able to participate. The sum of all three angles should now be 180 degrees. All three students must make sure that their own angle does not change size. After that, they can move away from the line and form a triangle. Will you manage to form the triangle?
The task description can be changed depending on whether the sum of a triangle’s angles is a new or a familiar theme. The task can be rephrased into a problem, e.g., as follows:
- Start at the line where you have created three angles (as above), and now form a triangle of the angles. What can you conclude about the sum of the angles of the triangle? OR
- You have been given a line with an angle of 180 degrees. How can you use your body to justify that the sum of a triangle’s angles is also 180 degrees?
You can illustrate the sum of a triangle’s angles using fingers, legs, or feet. Which way is easiest?

The idea is taken from Lumatikas material.