5.1 Basics of Geometry
Points, Lines and Planes
I.SectionObjectives
- Understand the undefined terms point, line and plane.
- Understand the defined terms, including space, segment, and ray.
- Identify and apply basic postulates of points, lines and planes.
- Draw and label terms in a diagram.
II.ProblemSolvingActivity-GlobalArchitecture
- Objective: The objective of this activity is to have students recognize the postulates connected with points,
lines and planes in real life architecture. - Here are the postulates.
- LinePostulate - There is exactly one line through any two points.
- PlanePostulate - There is exactly one plane that contains any three non- collinear points.
- Postulate - A line connecting points in a plane also lines with the plane.
- Postulate - the intersection of two distinct lines will be a single point.
- Postulate - the intersection of two planes is a line.
- You can either print the pictures, use computer displays or slides.
- The students need to use the following postulates and identify examples of each postulate as displayed in the
picture. - Students should be encouraged to use mathematical language as they describe and write about each example
of a postulate. - Figure01.01.01- The Guggenheim Museum in Spain http://en.wikipedia.org/wiki/Guggenheim_Museum_Bil
bao - Figure 01.01.02- Eiffel Tower http://en.wikipedia.org/wiki/File:Tour_Eiffel_Wikimedia_Commons.jpg
- Figure01.01.03- St. Basil’s Cathedral http://en.wikipedia.org/wiki/Saint_Basil%27s_Cathedral
III.MeetingObjectives
- Students found examples of points, lines and planes in each architectural figure.
- Students identified and applied the basic postulates associated with points, lines and planes.
IV.NotesonAssessment
- There are several different illustrations of each postulate in the architecture provided. This is an activity
where students are not only expected to be able to locate an example of each, but also where they need to use
mathematical language to write about how each postulate is shown in the architecture. - An example of this is in the picture of the Guggenheim. You can see that two of the planes intersect in exactly
one line. The sun is even shining directly on the line.
Chapter 5. Geometry TE - Problem Solving