Euclidean and Non-Euclidean Geometries Answers

Analyze the diagram below and complete the instructions that follow. Describe a way in which the diagram above illustrates the unique line postulate. A. Planes and intersect at line . B. There is exactly one line, m, through points B and D. C. There is exactly one plane, , through points A, B, and C. D. Plane contains points A and B and line . Please select the best answer from the choices provided

Through any three points there exists exactly one line. A. always B. sometimes C. never Please select the best answer from the choices provided

Analyze the diagram below and complete the instructions that follow. Name two red lines in the diagram that appear to be perpendicular. A. and B. and C. and D. No red lines are perpendicular. Please select the best answer from the choices provided

In Euclidean geometry, the sum of the measures of the interior angles of a pentagon is 540°. Predict how the sum of the measures of the interior angles of a pentagon would be different in spherical geometry. A. The sum would be greater than 540°. B. The sum would still be 540°. C. The sum would be less than 540°. D. The sum would less than or greater than, but never equal to, 540°. Please select the best answer from the choices provided

Spherical geometry is a form of __________ geometry. A. Euclidean B. plane C. non-Euclidean D. Archimedean Please select the best answer from the choices provided

Which postulate explains why a tripod will not tip over? A. A line contains at least two points. B. A plane contains at least three noncollinear points. C. Space contains at least four noncoplanar points. D. If two planes intersect, then their intersection is a line. Please select the best answer from the choices provided.

Analyze the diagram below and answer the question that follows. Image by Win The diagram above is an example of non-Euclidean geometry. What type of non-Euclidean geometry does it represent? A. spherical geometry B. Euclidean geometry C. hyperbolic geometry D. plane geometry Please select the best answer from the choices provided

Analyze the diagram below and complete the instructions that follow. Name three points that do not all lie in one of the planes shown in the diagram. A. G, F, and I B. E, F, and G C. H, I, and J D. , , and H Please select the best answer from the choices provided

A theorem is a statement in geometry that is accepted without proof.

If two planes cross one another, then their intersection is two lines.