* Pieces of shapes can be combined to form different 3-dimensional objects in spaces. ** *

Get some equilateral triangles.

Try taping the edges of 3 equilateral triangles around a point. *You get a convex tent ( tetrahedron).*

How about taping 4 or 5 triangles together?

*You still get convex tents, but with different shapes ( square pyramid, pentagonal pyramid). *

Try using 6 triangles.

*You get a flat surface! *

How about 7or 8 triangles?

*The surface ripples up and down. *

Triangles can also form other shapes... such as a dome.

**The Secret ... **

What makes taped triangles to create a flat surface?

The trick is: if the sum of the angles around a point = **360 ^{o}**, then the surface will be flat.

In our case, each angle of a equilateral triangle is **60 ^{o}**, so we need