AnswersA. CostelloWCA 5324 Geometry 1st Nine Weeks 26-27Euclidean Geometry

Euclidean Geometry Answers

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1
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Which statement represents the parallel postulate in Euclidean geometry, but not elliptical or spherical geometry?

A
Through a given point not on a line, there exists no lines parallel to the given line through the given point.
B
Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.
C
Through a given point not on a line, there exists more than one line parallel to the given line through the given point.
D
Through a given point not on a line, there exists exactly three lines parallel to the given line through the given point.
2
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How does a globe represent the fact that there are no parallel lines in elliptical geometry?

A
The equator is not parallel to any other latitudinal lines.
B
The North and South Poles are never connected by a geodesic.
C
The geodesics connecting the North and South Poles never intersect.
D
The geodesics connecting the North and South Poles intersect at both of the Poles.
3

Which surface represents a plane in hyperbolic geometry?

A
[Image: Sphere with grid lines....]
Option A
B
[Image: Curved plane with grid lines....]
Option B
C
[Image: Flat plane with grid lines....]
Option C
D
[Image: Cube with grid lines....]
Option D
4

Which statements about the sum of the interior angle measures of a triangle in Euclidean and non-Euclidean geometries are true? In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees. In Euclidian geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees. In Euclidian geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

A
In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees.
B
In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees.
C
In Euclidian geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees.
D
In Euclidian geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
E
In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
5

M.C. Escher was a famous artist who used unique viewpoints in his drawings that moved beyond flat plane surfaces. In his drawings, there are an infinite number of lines parallel to a given line through a point not on the given line. Which geometry did he use as his model?

A
hyperbolic geometry
B
Euclidean geometry
C
elliptical geometry
D
spherical geometry

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