Geometry (angle definitions)

vertical angles

2 angles in which the sides of 1 angle are opposite rays to the sides of another angle. Vertical angles are formed by intersecting lines (segments or rays). * vertical angles are equal in measure

linear angles

2 adjacent angles that come together to form a straight angle. Linear pairs of angles have a sum of 180 degrees

adjacent angles

2 angles that share a common vertex and a common side but they do not overlap. They do not share any common interior points

Supplementary angles

2 angles whose sum is 180 (therefore linear pairs of angles are supplementary)

complementary angles

2 angles whose sum is 90 degrees

alternate exterior angles theorem

if two parallel lines are cut by a transversal, then the alternate exterior angles are congruent

alternate interior angles theorem

if two parallel lines are cut by a transversal, then the alternate interior angles are congruent

full angles

angles that measure exactly 360 degrees (like a circle)

right angles

angles that measure exactly 90 degrees

acute angles

angles that measure less than 90 degrees

reflex angles

angles that measure more than 180 degrees but less than 360 degrees

obtuse angles

angles that measure more than 90 degrees but less than 180 degrees

normal segment to the line

distance between point and line

postulate about parallel lines and planes (1)

if a plane intersects two parallel planes, then the intersections are two parallel lines

theorem (overall, about the angles)

if the lines cut by the transversal are parallel, then the alternate interiors, alternate exteriors and corresponding angles will be congruent

vertical angles theorem

if two angles are vertical, then they are congruent

transversal

a line that intersect other lines (on the same plane) at different points

angle

a set of all the points that is the union of 2 rays having the same endpoint (when two rays share an endpoint both interior and exterior angles are created)

distributive

a(b+c)=ab+ac

associative

a+(b+c)=(a+b)+c

commutative

a+b=b+a

straight angles

angles that are created by the union of opposite rays. They measure exactly 180 degrees

congruent angles

angles that have the same measure. Therefore vertical angles are congruent

corresponding angles postulate

if two parallel lines are cut by a transversal, then the corresponding angles are congruent (the converse is true as well)

consecutive interior angles theorem

if two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary

postulate about parallel lines and planes (2)

if two planes are perpendicular to the same line, then the planes are parallel

angle bisectors

lines, rays, segments that divide an angle into two halves