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

A.Any two points determine a unique line

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

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

D.Any two lines intersect in exactly one point.

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Answer:

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Step-by-step explanation:

In spherical geometry the based on (two dimensional) geometric objects that are located on a spherical surface

The statement that is true in plane geometry but not true in spherical geometry is statement option D.

D. Any two lines intersect in exactly one point

The reason why the statement is correct is given as follows;

Spherical geometry is the geometry that has basic concepts being the point and great circles where the basic concepts in plane geometry is the point and the line

Therefore, while in plane geometry, a unique line is determined by two points, in  spherical geometry, a unique great circle is determined by two non polar points (points not at the poles)

However, 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 option D.

Learn more about spherical geometry here;

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