Question

Tell whether the following postulate or property of the plane euclidean geometry has a corresponding statement in spherical geometry. explain your reasoning or write the corresponding statement.

1. if two lines form vertical angles, then the angles are equal in measure.

2. if two lines meet a third line at the same angle, those lines are parallel.

3. three lines can form two triangles.

4. three non-parallel lines divide the plane into 7 separate parts.

Answer 1

When two lines form vertical angles, then the angles are equal in measure. This is true.

What is a vertical angle?

Vertical angles are angles opposite each other where the two lines cross. When two lines meet a third line at the same angle, those lines are not parallel.

There are no parallel lines in spherical geometry. On the globe, all the lines of longitude meet the equator at the right angle.

Three lines can form two triangles. This is true as three noncollinear points determine the triangle in spherical geometry.

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