Triangles + Parallel lines! (Proofs--Axioms + Theorems)

Definition of Congruent Triangles

Triangles whos corresponding sides and angles are congruent

SAS congruence axiom (only need to write that!)

If 2 sides and the included angle of one triangle are congruent to the corresponding 2 sides and included angle of another triangle then the triangles are congruent (dont need to write!)

CPCTC

(SHORT VER!): Corresponding parts of congruent triangles are congruent

Parallel lines

2 lines in the SAME PLANE that never intersect

Skew lines

2 lines NOT in the same plane that never intersect

If lines are parallel, then the corresponding angles are congruent

(AXIOM!)

if lines are parallel, then the alternate interior angles are congruent

(THEOREM)

If lines are parallel, then the same side interior angles are supplementary

(THEOREM)

Definition of perpendicular lines

lines are perpendicular if and only if the intersect to form right angles (If 2 lines intersect to form right angles they are perpendicular)

If two lines are perpendicular then they form congruent adjacent angles

yay!

If a transversal is perpendicular to one of the two parallel lines then it is perpendicular to the other line.

(THEOREM)

If two lines are perpendicular to the same line then they are perpendicular to eachother

(THEOREM)

If a transversal is perependicular to two lines then the lines are parallel

(THEOREM)

If two lines are parallel to the same line then they are parallel to each other

(THEOREM)

Euclid’s Axiom

Through a point not on a given line there is exactly one parallel and one perpendicular line to the given line.