Entry Task What are the first 3 steps for constructing a line through point P that is parallel to the line. Reflection Question: What are the main concepts.

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Presentation transcript:

Entry Task What are the first 3 steps for constructing a line through point P that is parallel to the line. Reflection Question: What are the main concepts or ideas that you learned in our class this week.

Spherical Geometry

Euclidean v. Non-Euclidean Geometry We mostly focus on Euclidean Geometry in this class. Things existing in the xy-plane (2 dimensions) Things on the xyz-coordinate system (3 dimensions) Today we will be exploring a type of Non-Euclidean Geometry called Spherical Geometry. Things existing on a sphere. There are other types of Non-Euclidean Geometry, such as hyperbolic and kinematic.

What is a sphere? A sphere is the set of all points in space that are the same distance from a given point, called the center. A great circle on a sphere is the largest circle around the sphere.

Lines and Line Segments What are our definitions of line and line segment? What would be a line on a sphere? What would be a line segment on a sphere? Explore Questions 5-15 on the handout. Use stickers for the points and rubber bands or string to represent the lines.

Triangles on a Sphere