1. A **point** is an ordered pair of real
numbers.

2. The **plane** is the set of all ordered
pairs of real numbers.

3. The **midpoint** between
(x_{1}, y_{1}) and (x_{2}, y_{2}) is

4. The **distance** between
(x_{1}, y_{1}) and (x_{2}, y_{2}) is

5. The **slope** between (x_{1},
y_{1}) and (x_{2}, y_{2}) is

6. A **line** is the set of all points whose
coordinates are solutions to a linear equation in two unknowns.

7. Two lines are **parallel** if their
slopes are the same.

8. Two lines are **perpendicular**
if their slopes are negative reciprocals of each other.

9. Given a line and a point, the point where
the line through the given point perpendicular to the given line
intersects the given line is called the **foot** of the point in
the line.

10. A **circle** has a center and all of
the points on the circle are the same distance from the center. This
distance is called the **radius** of the circle.

11. A **chord** of a circle is a line
segment whose endpoints are on the circle.

12. A **diameter** of a circle is a chord which goes through the center of the circle.

13. A **radius** of a circle is a line segment which goes from the center of a circle to a point on the circle.

14. A line that meets a circle in exactly
one point is called a **tangent** to the circle.

15. If A, B, and C are points on a
circle, then angle BAC is called an **inscribed angle**.

16. If O is the center of a circle and
B and C are points on the circle, then angle BOC is called a
**central angle**.

17. A **parallelogram** is a four
sided figure where the opposite sides are parallel.

18. A **rectangle** is a four sided
figure where all four angles are right angles.

19. A **rhombus** is a four sided figure
where all four sides have the same length.

20. A tirangle is an **isosceles**
triangle if two of its sides have the same length.

21. A triangle is an **equilateral**
triangle if all three sides have the same length.

22. A **median** of a triangle is a line
segment from one verted to the midpoint of the opposite side.

23. An **altitude** of a triangle is a
line segment from one vertex perpendicular to the opposite side

24. The point where the perpendicular
bisectors of the three sides of a triangle meet is called the
**circumcenter** of the triangle.

25. The circle which goes through all
three points of a circle is called the **circumscribed circle** or
**circumcircle**.

26. The point where the three angle
bisectors of a triangle meet is called the **incenter** of the
triangle.

27. The circle to which all three sides of
a triangle are tangent is called the **inscribed circle** or
**incircle**.

28. The point where the three medians of a
triangle meet is called its **centroid** or **center of
gravity**.

29.The point where the three altitudes
of a triangle meet is called the **orthocenter** of the triangle.

30. The **Euler line** of a triangle
goes through the circumcenter, the
centroid, and the
orthocenter.

31. The 9 point circle is centered at the midpoint of the Euler line and goes through the midpoints of the three sides, the feet of the altitudes, and the midpoints of the line segments between the orthocenter and the vertices of the triangle.

32. A **regular** polygon is one
where all the sides have the same length and all of the angles are
the same size.

33. The point where all of the
angle bisectors meet in a regular polygon is called the **center**
of the polygon.

34. A line segment from the center of a
regular polygon perpendicular to a side is called an **apothem**.