Points that lie on the same line
Collinear points
points that don't lie on the same line
Non-collinear points
objects which lie on the same plane
Coplanar objects
objects which don't lie on the same plane
Non-coplanar objects
statement that we accept without proof
Postulate
statement that we can prove using logic
Theorem
the intersection of two lines
Point
the intersection of two planes
Line
two coplanar lines that don't intersect
Parallel lines
two points and all points between them
Segment
segments with equal lengths
Congruent segments
point that divides a segment into two congruent segments
Midpoint
object that divides a segment into two congruent segments
Segment bisector
a part of a line that has only one endpoint
Ray
rays with the same endpoint which together form a line
Opposite rays
two rays joined by a common endpoint
Angle
common endpoint of two rays that form an angle
Vertex
angle with measure less than 90 degrees
Acute angle
angle with measure exactly 90 degrees
Right angle
angle with measure between 90 degrees and 180 degrees
Obtuse angle
angle with measure exactly 180 degrees
Straight angle
object (such as a ray or line) which divides an angle into two congruent angles
Angle bisector
a unit to measure angles which equals a fraction (1/360th) of a circle
Degree
the number of degrees in one-fourth of a circle
90
the number of degrees in one-half of a circle
180
the number of degrees in a circle
360
angles whose measures are equal
Congruent angles
coplanar angles with a common vertex and side, but no common interior points
Adjacent angles
a pair of angles whose measures add to 90 degrees
Complementary angles
a pair of angles whose measures add to 180 degrees
Supplementary angles
a pair of supplementary and adjacent angles
Linear pair
a pair of “opposite” angles formed by a pair of intersecting lines
Vertical angles
a statement that can be written in the form, "if p, then q.“
Conditional statement
the given information: part of a conditional statement found immediately after the word if
Hypothesis
the result of the hypothesis: part of a conditional statement found immediately after the word then
Conclusion
example showing a statement is not ALWAYS true, and is therefore false
Counterexample
statement obtained from a conditional statement by switching the hypothesis and the conclusion
Converse
statement obtained from a conditional statement by negating the hypothesis and the conclusion
Inverse
statement obtained from a conditional statement by negating AND switching the hypothesis and conclusion
Contrapositive
statement combining a conditional statement with its converse using the phrase "if and only if“
Biconditional statement MYP and PSC only
a diagram with two or more overlapping circles, used to show relationships between sets.
Venn Diagram
If p --> q is a true conditional and p is true, then q is true.
Law of Detachment
If p --> q and q --> r are true conditionals, then p --> r is true.
Law of Syllogism
lines that have a point in common
Intersecting lines
coplanar lines that do not intersect.
Parallel lines
lines that intersect at right angles
Perpendicular lines
lines that are non-coplanar and do not intersect
Skew lines
lines that intersect but are not perpendicular
Oblique lines
The steepness of a line expressed as a ratio, using any two points on the line
Slope
a line that intersects two other lines, at different points
Transversal
a pair of angles, both in the same position relative to two lines crossed by a transversal (that is, upper right, etc)
Corresponding angles
One pair of corresponding angles is 2 and ___
4
a pair of angles, both between two parallel lines and on opposite sides of the transversal
Alternate interior angles
One pair of alternate interior angles is 2 and ___
6
a pair of angles, both exterior to two parallel lines and on opposite sides of the transversal
Alternate exterior angles
One pair of alternate exterior angles is 1 and ___
5
a pair of angles, both between two parallel lines and on the same side of the transversal
Consecutive interior lines
One pair of consecutive interior angles is 2 and ___
3
a pair of angles, both exterior to two parallel lines and on the same side of the transversal
Consecutive exterior angles
One pair of consecutive exterior angles is 8 and ___
5