Unit 2 - Angles of Geometry - Proofs and Justifications Flashcards
Definition of Supplement Theorem
Linear pairs sum to 180
Angle Addition Postulate
When two angles are added together, they sum to the whole angle (for proofs, you can just say angle addition postulate).
Vertical Angle Theorem
Vertical angles are congruent
Corresponding Angle Postulate
If 2 parallel lines are cut by a transversal corresponding angles are congruent.
Alternate Interior Angle Postulate
If 2 parallel lines are cut by a transversal, alternate interior angles are congruent
(To identify, the lines create a z)
Consecutive Interior Angles Postulate
If 2 parallel lines are cut by the transversal, consecutive interior angles are supplementary.
Alternate Exterior Angles Theorem
If 2 parallel lines are cut by the transversal, alternate exterior angles are congruent.
Converse of the Corresponding Angles Postulate
If 2 lines are cut by a transversal such that corresponding angles are congruent, then the lines are parallel.
Converse of the Alternate Interior Angles Theorem
If 2 lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.
Converse of the Consecutive Interior Angles Theorem
If 2 lines are cut by a transversal such that consecutive interior angles are supplementary then the lines are parallel.
Converse of the Alternate Exterior Angles Theorem
If 2 lines are cut by a transversal such that alternate exterior angles are congruent, then the lines are parallel.
Converse of the Perpendicular Transversal Theorem
If 2 lines are perpendicular to the same lines, then they are parallel to each other.
What are the 5 ways that proves that a pair of lines are parallel?
- Converse of Corresponding Angle Postulate
- Converse of Alternate Interior Angle Theorem
- Converse of Alternate Exterior Angle Theorem
- Converse of Consecutive Interior Angle Theorem
- Converse of the Perpendicular Transversal Theorem
What are the two reasons why something is not parallel?
- Congruent angles form, but not because of the 5 reasons
- Found on COMPLETELY different transversals
Why do we use auxiliary lines?
Often in geometry, it is helpful to modify the figure in order to find certain info. It is never acceptable to change of the original parts of the figure, but it is allowed to draw in dotted lines that help demonstrate something.
