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.
if 2 lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
if 2 sides of 2 adjacent acute angles are perpendicular; then the angles are complementary.
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.
is a segment, ray, line, or plane that intersects a segment at its midpoint.
a ray that divides an angle into two adjacent angles that are congruent.`
two angles whose sides form two pairs of opposite rays.
two adjacent angles whose non-common sides form one pair of opposite rays.
has two parts: a hypothesis and a conclusion.
conditional statement where "if" is the hypothesis & then is the conclusion.
lines that are coplanar and do not intersect.
not coplanar and do not intersect.
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.
switches the hypothesis and the conclusion.
makes the hypothesis and conclusion negative.
negation of the converse.
a geometric drawing using a limited set of tools, using a straight edge.
an un-proven statement that is based on observations.
example that shows a conjecture is false.
no dimension, represented by a small dot.
extends in one dimension. usually represented by a straight line w/two arrowheads to indicate that the line extends without end in two directions.
extends in 2 dimensions. usually represented by a shape that looks like a table top or wall.
set of points a figure has in common.
rules accepted without proof.
real #s that corresponds to a point.
consists of different rays that have the same initial point.
sides of an angle.
initial point of angle.
between points that lie on each side of the angle.
not on the angle or inits interior.
share a common vertex & side, but have no common initial points.
intersect to form a right angle.
if a = b, then a + c = b + c.
ex: x = y, then x + 2 = y + 2.
if a = b then a - c = b - c
If a=b, then ac = bc
If a=b, then a/c=b/c
if A = B then a can be substituited for b in an equation or expression.
For any real number a, a=a
If a = b, then b = a
If a = b and b = c, then a = c.
linear pair postulate
if 2 angles form a linear pair, then they are supplementary
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.
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.