Euclidean and Non-Euclidean Geometries

Question 1

Analyze the diagram below and complete the instructions that follow. Describe a way in which the diagram above illustrates the unique line postulate.

Revolt · Accepted Answer

There is exactly one line, m, through points B and D.

Question 2

Through any three points there exists exactly one line.

Revolt · Accepted Answer

sometimes

Question 3

Analyze the diagram below and complete the instructions that follow. Name two red lines in the diagram that appear to be perpendicular.

Revolt · Accepted Answer

No red lines are perpendicular.

Question 4

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.

Revolt · Accepted Answer

The sum would be greater than 540°.

Question 5

Spherical geometry is a form of __________ geometry.

Revolt · Accepted Answer

non-Euclidean

Question 6

Which postulate explains why a tripod will not tip over?

Revolt · Accepted Answer

A plane contains at least three noncollinear points.

Question 7

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?

Revolt · Accepted Answer

hyperbolic geometry

Question 8

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.

Revolt · Accepted Answer

G, F, and I

Question 9

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

Revolt · Accepted Answer

F

Question 10

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

Revolt · Accepted Answer

F

Euclidean and Non-Euclidean Geometries Answers

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