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Indicate whether each statement is True (T) or False (F). a If a plane contains one of two skew lines, it contains the other. b If a line and a plane never meet, they are parallel. c If two parallel lines lie in different planes, the planes are parallel. d If a line is perpendicular to two planes, the planes are parallel. e If a plane and a line not in the plane are each perpendicular to the same line, then they are parallel to each other.

Prove Theorem 46: Two intersecting lines determine a plane. (Write a paragraph proof.)

From any point on a line perpendicular to a plane, two lines are drawn oblique to the plane. If the foot of the perpendicular is equidistant from the feet of the oblique lines, prove that the oblique segments are congruent.

If two points in space are equidistant from the endpoints of a segment, will the line joining them be the perpendicular bisector of the segment? Explain.

Prove that if a line is perpendicular to the plane of a circle and passes through the circle's center, any point on the line is equidistant from any two points of the circle.