We often hear people in physics and mathematics talking about 4-dimensional, 5-dimensional spaces, etc... so what are those spaces? how do we picture these high dimensional spaces?

### What does a 4-dimensional space look like?

We often hear people in physics and mathematics talking about 4-dimensional, 5-dimensional spaces, etc... so what are those spaces? how do we picture these high dimensional spaces?

### Similar triangles

Today, we are going to learn about

*similar triangles*. We will use similar triangles to give a proof of Pythagorean Theorem.

### Caveman's multiplication

### Morley's Theorem

In a triangle $ABC$, draw the trisectors of the angles $A$, $B$, $C$. These trisectors intersect at $A'$, $B'$ and $C'$ as in the figure below. Prove that the triangle $A'B'C'$ is an

*triangle.***equilateral**
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