Advanced geometry topic 2

issy highschool advanced geometry definitions 2.1 - 2.3

Transversal

a line that intersects two or more lines.

corresponding angles

angles on the same side of the transversal and in the same position

alt interior angles

interior angles, non-adjacent and on opposite sides of the transversal

consecutive (same side) interior angles

interior angles that are on the same side of the transversal

consecutive (same side ) exterior angles

exterior angles that are on the same side of the transversal

if two parallel lines are cut by a transversal, then:

corresponding angles are congruent

alt interior angles are congruent

alt exterior angles are congruent

consecutive same side interior angles are supplementary (add to 180)

consecutive same side exterior angles are supplementary

vert angles are always congruent and angles that form a linear pair are always supplementary

same side interior consecutive angles postulate:

if a transversal intersects two parallel lines then same side interior angles are supplementary

Same side exterior consecutive angles postulate:

if a transversal intersects two parallel lines then same side exterior angles are supplementary

alt interior angles theorem

if a transversal intersects two parallel lines, then alternate interior angles are congruent

corresponding angles theorem

if a transversal intersects two parallel lines then corresponding angels are congruent.

alt exterior angles theorem

if a transversal intersects two parallel lines, then the alt exterior angles are congruent.

corresponding angles converse

if two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.

alt interior angles converse

if two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel.

alternate exterior angles converse

if two lines are cut by a transversal so that a pair of alt exterior angles are congruent, then the lines are parallel.

consecutive interior angles converse

if two lines are cut by a transversal so that a pair of consecutive interior angles are supplementary, then the lines are parallel.

consecutive exterior angles converse

if two lines are cut by a transversal so that a pair of consecutive exterior angles are supplementary, then the lines are parallel.

Theorem 2-8

if two lines are parallel to the same line, then they are all parallel to each other.

Theorem 2-9

if two lines are perpendicular to the same line, then they are parallel to each other.

Triangle sum theorem

the sum of the measures of the angles of a triangle is 180°

M<A + M<B + M<C =180°

Triangle exterior angle theorem

an exterior is always equal to the sum of the two non-adjacent interior angles.

Ex: M<1 = M<2+M<3