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AoPS

AoPS. Introduction to Geometry. Chapter 1: What’s in a Name?. Point. A dot. A speck. No up and down, no right and left. Can’t move any amount in any direction. 0 dimensions P . Point. A dot. A speck. No up and down, no right and left. Can’t move any amount in any direction.

AoPS

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Presentation Transcript

1. AoPS Introduction to Geometry

2. Chapter 1: What’s in a Name?

3. Point A dot. A speck. No up and down, no right and left. Can’t move any amount in any direction. 0 dimensions P 

4. Point A dot. A speck. No up and down, no right and left. Can’t move any amount in any direction. 0 dimensions P  You get bored so you walk from one point to another on a straight path

5. Point A dot. A speck. No up and down, no right and left. Can’t move any amount in any direction. 0 dimensions P  You get bored so you walk from one point to another on a straight path AB denotes a segment with endpoints A and B.

6. Line Segment You get bored so you walk from one point to another on a straight path AB denotes a segment with endpoints A and B. There are infinitely many points between any 2 points – one special point is the midpoint – it is equidistant from the endpoints.

7. Ray If you’re not happy just going from A to B, you can keep going past point B. If you keep going forever, you will make a ray. A B AB

8. Line We could continue forever in both directions. The result is a line. B k A AB Sometimes we use a lowercase letter to describe a line, such as k in the figure.

9. Collinear Points If three or more points are on the same line we say they are collinear.

10. Concurrent Lines If 3 or more lines pass through the same point, we say the lines are concurrent.

11. Plane Once we have the freedom to move off the path and move around on a surface, we’re up to two dimensions. we might call our dimensions left-right and up-down. If the page extended forever in every direction, we’d call it a plane.

12. A chord is? What an arc??? Circle What is a What is a tangent? sector? a secant?? a segment??

13. AB arc AB A B

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