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Lines And Angles

The following are some important Axioms and Theorems from Lines and Angles

 

Incidence Axiom 1

Through a given point, there pass infinitely many lines

 

Incidence Axiom 2

For any two points, there is exactly one line containing them.

 

Incidence Axiom 3

A line contains infinitely many points.

 

Incidence Axiom 4

If two points of a line are in a given plane, then the line is in the plane.

 

Incidence Axiom 5

If two planes intersect, then they intersect in exactly one line.

 

Parallel Line Axiom

Two distinct lines can not have more than one point in common.

 

Parallel line Theorem

Two lines which are both parallel to the same line are parallel to each other.

 

Angle Measure Axiom

Every angle has a measure

 

Congruent Angle Measure Axiom

Two congruent angles have the same measure, and conversely two angles of measure are congruent.

 

Linear Pair Axiom

If a ray stands on a line, then the sum of the two adjacent angles so formed is 180º. Conversely, if the sum of the two adjacent angles is 180º, then the non common arms of the angles are two opposite rays.

 

Vertically Opposite angles

If two lines intersect, then the vertically opposite angles are equal.

 

Corresponding Angles Axiom

It a transversal intersects two parallel lines, then each pair of corresponding angles is equal. Conversely, if a transversal intersects two lines, making a pair of corresponding angles equal, then the lines are parallel.

 

Alternate interior angles Theorem

If a transversal intersects two parallel lines, then each pair of alternate interior angles are equal. Conversely, if a transversal intersects two lines in such a way that a pair of alternate interior angles is equal, then the two lines are parallel.

 

Consecutive interior angles Theorem

If a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary. Conversely, if a transversal intersects two lines in such a way that a pair of consecutive interior angles is equal, then the two lines are parallel.