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 (x1, y1) and (x2, y2) is
4. The distance between (x1, y1) and (x2, y2) is
5. The slope between (x1, y1) and (x2, y2) 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.