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1.4 Segments, Rays, Parallel Lines and Planes

This educational resource delves into the fundamental concepts of segments, rays, parallel lines, and planes in geometry. A segment consists of two endpoints and all points between them, while a ray is defined by one endpoint and extends infinitely in one direction. The distinction between parallel lines, which exist in the same plane without intersecting, and skew lines, which are non-coplanar and never meet, is clarified. Visual examples and terminology aid in comprehension, making this a vital guide for students exploring geometric relationships.

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1.4 Segments, Rays, Parallel Lines and Planes

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  1. 1.4 Segments, Rays, Parallel Lines and Planes 1.4 Segments, Rays, Parallel Lines and Planes “I have always grown from my problems and challenges.” -Carol Burnett “I have always grown from my problems and challenges.” -Carol Burnett

  2. Terms A segment is the part of a line consisting of two endpoints and the points between them. A ray is one endpoint and all of the points on one side of the endpoint. Opposite rays are two collinear rays with the same endpoint. Opposite rays always form a line. A B

  3. Naming Name the segments and rays. Three segments: Four rays: C B B A

  4. Parallel… ?? • Visualize a plane (it’s flat). • Think of two lines that are both in the plane. • Now make sure that the two lines do not intersect. [PARALLEL] • Notice that the lines are coplanar (in the same plane). • Now start over with a blank plane. • Think of one line in the plane. • Think of another line that can’t be included in the plane, even if you rotated the plane (remember: the plane has to be flat – it can’t turn a corner). • Now make sure that those two lines do not intersect. • This is different than parallel because the lines are noncoplanar (not in the same plane).

  5. Terms Parallel lines are coplanar lines that do not intersect. Skew lines are noncoplanar; therefore, we can’t say they’re parallel, but we can say that they do not intersect. Do skew lines “look” parallel?

  6. Terms Parallel planes are planes that do not intersect. *Note: A line and a plane that do not intersect with each other are also parallel. Example: 1. Identify two parallel planes. 2. Identify a plane and a line that are parallel. G H A C J I D B

  7. 1.4 Segments, Rays, Parallel Lines and Planes HW: 4-15, 16-22 EVEN, Page 30 #1-19 ODD (linear equations review) Terms: segment, ray, opposite rays, parallel lines, skew lines, parallel planes “I have always grown from my problems and challenges.” -Carol Burnett

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