Geometry Theorms, Postulates, Etc.

52 terms

right angle congruence thereom

all right angles are congruent.

congruent supplements thereom

if 2 angles are supplementary to the same angle or to congruent angles, then they are congruent to each other.

congruent complements thereom

if 2 angles are complementary to the same angle or to congruent angles, then they are congruent to each other.

vertical angles thereom

vertical angles are congruent.

theorem 3.1

if 2 lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

theorem 3.2

if 2 sides of 2 adjacent acute angles are perpendicular; then the angles are complementary.

theorem 3.3

if 2 lines are perpendicular then they intersect to form 4 right angles.

alternate interior angles theorem

if 2 parallel lines are cut by a transversal then the pairs of consecutive interior angles are supplementary.

alternate exterior angles thereom

if 2 parallel lines are cut by a transversal, alternate exterior pairs are congruent.

perpendicular transversal theorem

if a transversal is perpendicular to one of 2 parallel lines, it is perpendicular to the other one.

segment bisector

is a segment, ray, line, or plane that intersects a segment at its midpoint.

angle bisector

a ray that divides an angle into two adjacent angles that are congruent.`

vertical angles

two angles whose sides form two pairs of opposite rays.

linear pair

two adjacent angles whose non-common sides form one pair of opposite rays.

conditional statement

has two parts: a hypothesis and a conclusion.

if/then form

conditional statement where "if" is the hypothesis & then is the conclusion.

parallel lines

lines that are coplanar and do not intersect.

skew lines

not coplanar and do not intersect.

parallel planes

planes that dont intersect.

law of detachment

if p to q is a true statement, & p is true, then q is true.

law of syllogism

if p to q is a true statement & q to r is a true statement then p to r is true.

converse

switches the hypothesis and the conclusion.

inverse

makes the hypothesis and conclusion negative.

contrapositive

negation of the converse.

construction

a geometric drawing using a limited set of tools, using a straight edge.

conjecture

an un-proven statement that is based on observations.

counterexample

example that shows a conjecture is false.

point

no dimension, represented by a small dot.

line

extends in one dimension. usually represented by a straight line w/two arrowheads to indicate that the line extends without end in two directions.

plane

extends in 2 dimensions. usually represented by a shape that looks like a table top or wall.

intersection

set of points a figure has in common.

postulate

rules accepted without proof.

coordinate

real #s that corresponds to a point.

angle

consists of different rays that have the same initial point.

rays

sides of an angle.

vertex

initial point of angle.

interior

between points that lie on each side of the angle.

exterior

not on the angle or inits interior.

share a common vertex & side, but have no common initial points.

perpendicular lines

intersect to form a right angle.

if a = b, then a + c = b + c.
ex: x = y, then x + 2 = y + 2.

subtraction property

if a = b then a - c = b - c

multiplication property

If a=b, then ac = bc

division property

If a=b, then a/c=b/c

substituiton property

if A = B then a can be substituited for b in an equation or expression.

reflexive property

For any real number a, a=a

symmetric property

If a = b, then b = a

transitive property

If a = b and b = c, then a = c.

linear pair postulate

if 2 angles form a linear pair, then they are supplementary

parallel postulate

if there is a line and a point not on that line, then there is exactly one line through the point parallel to the given line.

perpendicular postulate

if there is a line, and a point not on that line, then there is exactly one line thru the point perpendicularto the given line.

corresponding angles postulate

if 2 parallel linees are cut by a transversal, corresponding angle pairs are congruent.