
Lesson 7: Non-Euclidean Geometries Quiz

Passage
•
Mathematics
•
12th Grade
•
Hard
+2
Standards-aligned
Wayground Content
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15 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Who are credited with the independent discovery of Hyperbolic Geometry?
Euclid, Bolyai, and Lobachevsky
Euler, Fermat, and Poincaré
Pythagoras, Newton, and Gauss
Archimedes, Descartes, and Riemann
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the characteristic postulate of Hyperbolic Geometry?
Through a point P not on a line l, there exists exactly one line parallel to l.
Through a point P not on a line l, there exist at least two lines parallel to l.
Through a point P not on a line l, there is no line parallel to l.
Through a point P not on a line l, there exist infinitely many lines parallel to l.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is Poincaré's model of Hyperbolic Geometry?
Points are ordinary points inside the unit circle, lines are diameters of the circle or arcs of circles perpendicular to the boundary.
Points are points on the surface of a 2-dim sphere with antipodal points identified, lines are straight lines extending to infinity.
Points are points on the surface of a 2-dim sphere with antipodal points identified, lines are great circles (longitudes or meridians).
Points are ordinary points inside the unit circle, lines are straight lines extending to infinity.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In Hyperbolic Geometry, what is the sum of the angles of a triangle?
Equal to 180 degrees
Depends on the type of triangle
Greater than 180 degrees
Less than 180 degrees
Tags
CCSS.2.G.A.1
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What did Enrico Beltrami prove in 1868?
He proved the existence of similar triangles in Hyperbolic Geometry
He proved the equivalence of Euclidean and non-Euclidean (hyperbolic) geometries
He proved the existence of parallel lines in Hyperbolic Geometry
He proved the existence of infinitely many lines parallel to a given line through a given point in Hyperbolic Geometry
Tags
CCSS.4.G.A.1
CCSS.HSG.CO.A.1
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the characteristic postulate of Elliptic Geometry?
Through a point P not on a line l, there exist infinitely many lines parallel to l.
Through a point P not on a line l, there is no line parallel to l.
Through a point P not on a line l, there exist at least two lines parallel to l.
Through a point P not on a line l, there exists exactly one line parallel to l.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is Riemann's spherical model of Elliptic Geometry?
Points are points on the surface of a 2-dim sphere with antipodal points identified, lines are straight lines extending to infinity.
Points are ordinary points inside the unit circle, lines are diameters of the circle or arcs of circles perpendicular to the boundary.
Points are points on the surface of a 2-dim sphere with antipodal points identified, lines are great circles (longitudes or meridians).
Points are ordinary points inside the unit circle, lines are straight lines extending to infinity.
Tags
CCSS.HSG.CO.A.2
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