M108 MODERN GEOMETRY

What is the equivalence of point, line and plane in spherical geometry?

• point, line and plane

• point, great circles and spheres

• point, arcs and curves

• point, angles and triangles

What are the points opposite to each other in a sphere?

• endpoints

• anecdotal points

• antipodal points

• spherical points

How can you describe the sum of interior angles in Euclidean geometry?

• Equal to 180º

• Less than 180 º

• 540 º and more

• Greater than 180 º but less than 540 º

What is study was based on astronomy of Earth and their need to be able to measure time accurately?

• Euclidean geometry

• Hyperbolic Geometry

• Spherical Geometry

• Synthetic Geometry

How many times will two parallel lines meet in spherical geometry?

• 1

• 2

• 3

• parallel lines do not exist

What is the shortest path between two point in spherical geometry?

• arc 

• diameter

• line segment           

• radius

How many right angles will be formed by perpendicular lines in Euclidean geometry?

• 1

• 2

• 4

• 8

What is the measure of each angle in equilateral triangle in Euclidean geometry?

• 60º

• 180º

• 540º

• may vary

What is the branch of mathematics that deals with the relationships between geometric figures and the images, or mappings, that result from projecting them onto another surface?

• Euclidean geometry

• Hyperbolic Geometry

• Spherical Geometry

• Projective Geometry

Who popularized one hexagon theorem in projective geometry?

• Blaise Pascal

• Girard Desargues

• Pappus of Alexandria

• None of the choices