Please explain with another simple example
If you didn't, how would you measure i or r?
What would you do in the case of a curved surface?
The normal, which is perpendicular to the plane forming the interface between media (e.g. solid and gas), is simply a reference. The maximum transmission of light comes when the beam (photons) is parallel with the normal.
The normal is indeed a reference =) We need the normal (as what Astronuc said, perpendicular to the plane) to measure indexes .
When we develop the maths to describe the physics we try to make the maths as simple as possible. So the theory dictated that if we use the normal to the interface between the two media the maths will be much easier and natural to the real situation. You can also see that, using the normal as the reference for the angles, when the incident angle is zero the refraction angle will also be zero, which makes the most sense does'nt it? Refraction problems were also initially solved with graphical techniques in which case the normal were used in the diagrams (seee history of Willebrord van Roijen Snell - also called Snellius).
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