Foundations of Geometry Notes

Watch the video “Geometry Basics” Section B and answer questions #1 - 11.

Section B: Points, Lines, Planes, and Space

  1. What are the building blocks of Geometry? ______
  1. A ______has no length or width.
  1. A ______extends infinitely in both directions.
  1. A ______begins at one point and extends endlessly in one direction.
  1. ______points are points that lie on one line.
  1. A ______is a part of a line or ray between two points.
  1. A ______is the exact middle of a segment.
  1. When a line, ray, segment, or plane crosses a segment at its midpoint, it is said to ______the segment.
  1. A ______is a flat surface that extends infinitely in all directions.
  1. Two ______lines can either intersect or be parallel.
  1. ______is the set of all points in three dimensions.

Postulates and Theorems

  1. A ______is an assumption accepted without proof.
  1. A ______is a statement we can prove.

Because Geometry is a visual math, the best thing you can do to start off any problem is to model it with a diagram. Model the postulates below and see if you can figure out what word will complete the postulate.

  1. Postulate: Through any two points, there is one and only one ______.
  1. Postulate: Through any three non-collinear points, there is only one unique ______.
  1. Postulate: If two planes intersect, they intersect in a ______.
  1. Postulate: If two lines intersect, they intersect at a unique ______.

Notation

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  1. When naming points, we use a capital letter. Name the four points on the line in figure 1.
  1. When naming lines, we use (1) an italic letter not assigned to a point (lowercase) or (2) any two points on the line with the line symbol above it (). The order of the points doesn’t matter. Name the linein figure 1 using both methods.
  1. When naming rays, we use the endpoint (where the ray begins) and any other point on the ray with the ray symbol () above it. The ray symbol will always point to the right regardless of which direction the ray extends. The endpoint must always be the first letter of the name. Name the ray in figure 2.
  1. Opposite rays are two rays that have a common endpoint and form a line or straight angle. Name the ray that is opposite in figure1.
  1. When naming segments, we use the endpoints (where the segment starts and ends) with the segment symbol above it. When a segment name is written without the symbol, it is asking for the length of the segment. Name the segment in figure 3. How would you write “the length of” the segment?
  1. When naming planes, we use (1) an uppercase letter not assigned to a point or (2) at least three non-collinear points (only one has to be non-collinear). Name the plane at right using both methods.
  1. When two or more points are on the same line, we say they are collinear (“co” meaning to share and “linear” meaning line). Name three collinear points in the plane in figure 4.
  1. When points or lines are on the same plane, we say they are coplanar (“co” meaning to share and “planar” meaning plane). Name four coplanar points in the plane in figure 4.

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