Identify the geometries (Euclidean, hyperbolic, and/or spherical) in which each statement is true. Given a line and a point,

Question

Identify the geometries (Euclidean, hyperbolic, and/or spherical) in which each statement is true.
Given a line and a point, there is a unique line containing the point that is perpendicular to the line.
Two lines always intersect in a single point.
Given two parallel lines and a transversal, alternate interior angles are necessarily congruent.
Given triangles ABC and DEF, if AB = DE, BC = EF, and angle B is congruent to angle E, then triangle ABC is congruent to triangle DEF.

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