Modern Geometry

The angles of parallelism in hyperbolic geometry are neither right nor obtuse.

• True

• False

In hyperbolic geometry, if 𝑙 is any line and P is any point not on 𝑙, then there are exactly two lines through P that do not intersect 𝑙 and that make equal acute angles with the perpendicular from P to 𝑙.

• True

• False

The hyperbolic axiom states that there exist a line 𝑙 and a point P not on 𝑙 such that at least two distinct lines parallel to 𝑙 pass through P.

• True

• False

The elliptic axiom states that there are no lines parallel to the given line.

• True

• False

In hyperbolic geometry, all triangles have angle sum less than 𝜋 radians.

• True

• False

There are no more than two ideal points on a hyperbolic line.

• True

• False

In elliptic geometry, the sum of the measures of the angles of any triangle is less than 𝜋.

• True

• False

In elliptic geometry, the summit angles of a Saccheri quadrilateral are congruent and obtuse.

• True

• False

A spherical line is a semicircle.

• True

• False

A great circle is formed by the intersection of the sphere and a plane that goes through the origin 𝟎.

• True

• False