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vertical angles

When angles are across from one another in an X pattern,Vertical angles are congruent

perpendicular lines

If two lines intersect, and one of the angles is 90°, then the lines are perpendicular.

perpendicular bisector

If a line or a segment is perpendicular to another segment at its midpoint,The distances of any point on the perpendicular bisector from both endpoints of the line being bisected are the same. If any point on the perpendicular bisector is connected to the endpoints of the segment being bisected, the angles formed at the endpoints are congruent.

coplanar lines

Two lines that are in the same plane are

skew lines

Two lines that are in the same plane are called coplanar lines; otherwise they are referred to as

intersecting lines

When they have one common point, they are

parallel lines

If two lines are on the same plane and have no common points then they are

concurrent lines

If a set of two or more lines intersect in only one point, concurrent lines are another form of intersecting lines

transversal

If a line intersects a set of parallel lines it is

vertical angles theorem

vertical angles have an equal measure

perpendicular lines theorem

If two lines are perpendicular, then they form congruent adjacent angles

If two lines form congruent adjacent angles, then the lines are perpendicular.

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complimentary

If two lines form congruent adjacent angles, then the lines are perpendicular.

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complimentary

the properties of a perpendicular bisector

The distances of any point on the perpendicular bisector from both endpoints of the line being bisected are the same.

If any point on the perpendicular bisector is connected to the endpoints of the segment being bisected, the angles formed at the endpoints are congruent.

If any point on the perpendicular bisector is connected to the endpoints of the segment being bisected, the angles formed at the endpoints are congruent.

congruent angles when parallel lines are cut by a transversal

Alternate Interior Angles are located between the parallel lines and on opposite sides of the transversal.

difference between Euclidean and Non-Euclidean Geometry

Euclidean Geometry is all on a flat surface

Spherical geometry is an example of non-Euclidean geometry.

Spherical geometry is an example of non-Euclidean geometry.