Question

Which statement is true in plane geometry but not true in spherical geometry?

Any two lines intersect in exactly one point.

A triangle can be drawn through any three non-collinear points.

The sum of the measures of the angles in a triangle is 360°.

Any two points determine a unique line.

Answer 1

Answer:

Any two lines intersect in exactly one point.

Step-by-step explanation:

Answer 2

D. Any two points determine a unique line.

In spherical geometry

• There are no parallel lines, there are no straight lines.  Therefore, in spherical geometry, a great circle is comparable to a line.  
• There are no straight lines in spherical geometry. Instead, the shortest distance from one point to the next lying on a sphere is along the arc of a great circle.
• On a sphere, the angle between two curved arcs is measured by the angle formed from the intersection of the lines lying tangent to the two arcs.

In Plane geometry:

• Given any two points, we can draw exactly one line that passes through both of them. In other words, two points determine a line.

• When two lines intersect, they share a single point.
• When two lines don’t intersect, they are parallel, which means that they remain the same distance from each other everywhere.

So, we have

Any two lines in plane geometry intersect in exactly one point

Any two intersecting great circles intersect at two points

Therefore, the correct option is D.

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