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## Points, Lines, and Planes

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**Points, Lines, and Planes**Sections 1.1 & 1.2**Definition of a Point**A point has no dimension. It is represented by a dot. A point is symbolized using an upper-case letter.**Definition: Line**A line has one dimension. (infinite length) A line is named using any two points on the line with a two sided arrow above them like this: . It can also be named by using a lower-case cursive letter. Through any two points, there is exactly one line.**Definition: Collinear points**points that lie on the same line.**Definition: Between**If a point is between two other points then that means it must also be collinear with the other two points.**Definition: Plane**A plane has two dimensions. It is represented by a shape that looks like a floor or a wall, but it extends infinitely in length and width. Any three non-collinear points can define a plane. A plane is named using the word plane with 3 non-collinear points or with an upper-case cursive letter.**Definition: Coplanar:**Coplanar points are points that lie (or could lie) in the same plane.**Definition: Line Segment:**The line segment consists of two endpoints and all the points between them. A line segment is named using both endpoints with a line above them like this: . and refer to the same line segment.**Definition: Ray**The ray consists of an endpoint and all points on a line in the opposite direction. A ray is named using its endpoint first and then any other point on the ray with a ray symbol pointing to the right above them like this: . and do not refer to the same ray.**Definition: Opposite Rays:**If point C lies on line AB between A and B, then ray CA and ray CB are opposite rays. Two opposite rays make a line.**Definition: Intersection:**The intersection of two or more figures is the set of points the figures have in common. The intersection of 2 different lines is a point. The intersection of 2 different planes is a line.**Definition: Distance:**The distance between points A and B, also known as the length of line segment AB is the absolute value of the difference of the coordinates of A and B. In other words, distance is many units apart the points lie. The distance from A to B, or the length of Is written as AB. (No symbol above).**Definitions:**Postulate: A rule that is accepted without proof. Theorem: A rule that can be proven.**The Ruler Postulate:**The points on a line can be matched one to one with the real numbers.**Segment Addition Postulate:**If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C.**Definition: Congruent Segments:**Line segments that equal (=)length are called congruent (segments. To show that two segments are congruent in a drawing we use tick marks. A B C D**PRACTICE: A1**• p.5: 1-12, 17-22 • p.12: 6-10(even), 16-30(even)