Parallel Theorems

Question 0

If two lines are cut by a transversal such that two interior angles on the same side of the transversal are supplementary,

Answer 0

then the lines are parallel.

Question 1

The measure of an exterior angle of a triangle

Answer 1

is greater than the measure of either remote interior angle.

Question 2

If two lines are cut by a transversal such that two exterior angles on the same side of the transversal are supplementary,

Answer 2

then the lines are parallel.

Question 3

If two coplanar lines are perpendicular to a third line,

Answer 3

then they are parallel.

Question 4

If two parallel lines are cut by a transversal,

Answer 4

then any pair of the angles formed are either congruent or supplementary.

Question 5

If two parallel lines are cut by a transversal,

Answer 5

then each pair of interior angles on the same side of the transversal are supplementary.

Question 6

If two parallel lines are cut by a transversal,

Answer 6

then each pair of exterior angles on the same side of the transversal are supplementary.

Question 7

In a plane, if a line is perpendicular to one of two parallel lines,

Answer 7

then it is perpendicular to the other.

Question 8

If two lines are parallel to a third line,

Answer 8

then they are parallel to each other.

Question 9

If a line is perpendicular to two distinct lines that lie in a plane and that pass through the foot,

Answer 9

then it is perpendicular to the plane.

Question 10

If a plane intersects two parallel planes,

Answer 10

then the lines of intersection are parallel.

Question 11

If two planes are perpendicular to the same line,

Answer 11

then they are parallel to each other.

Question 12

If a line is perpendicular to one of two parallel planes,

Answer 12

then it is perpendicular to the other plane as well.

Question 13

If two planes are parallel to the same plane,

Answer 13

then they are parallel to each other.

Question 14

If two lines are perpendicular to the same plane,

Answer 14

then they are parallel to each other.

Question 15

If a plane is perpendicular to one of two parallel lines,

Answer 15

then it is perpendicular to the other line as well.