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The word “geometry” comes from the ancient Greek words “geo” meaning Earth and “metron” meaning measurement. It is probably the oldest field of mathematics, because of its usefulness in calculating lengths, areas, and volumes of everyday objects.

The study of geometry has evolved a great deal during the last 3,000 years or so. Like all of mathematics, what’s really important in geometry is reasoning, making sense of problems, and justifying your solutions.

The mathematician Henri Poincaré said that

Geometry is the art of good reasoning from bad drawings.

This insight should guide your study in this chapter. You should never trust a drawing. You might find that one line segment appears to be longer than another, or an angle looks like it might be 90 degrees. But “appears to be” and “looks like” are simply not good enough. You have to reason through the situation and figure out what you know for sure and why you know it.