Topic 1 Foundations of Geometry

point

geometric element, indicates location, 0 dimensions

line

collection of points, straight path, continues infinetly in both directions

line segment

part of a line that contains every point of a line between its endpoints

ray

a line with a single endpoint that extends infinitely in one direction

Collinear

points on the same line

equidistant

equally distant

angle

A figure formed by two rays with a common endpoint

opposite rays

two rays that have a common endpoint and form a line whose angle measure is 180 degrees

congruent

Having the same size and shape

tick marks

Marks used on a figure to indicate congruent segments

arc markings

marks used on a figure to indicate congruent angles

vertex

A point where two or more straight lines meet forming an angle

Distance Formula

used to find the length between two points

midpoint formula

used to find the coordinates of the point that is the midpoint of two other endpoints

parallel lines

Lines in the same plane that never intersect. Their slopes are equal.

perpendicular lines

Lines that intersect to form right angles. Their slopes are the negative reciprocal of each other.

Segment Addition Postulate

If B is between A and C, then AB + BC = AC. The sum of the parts = the whole

Angle Addition Postulate

If S is in the interior of

vertical angles

are opposite (non-adjacent) angles of two intersecting lines

linear pair

A pair of adjacent angles whose noncommon sides are opposite rays forming a straight line

Addition Property of Equality

If a = b, then a + c = b + c (add the same thing to both sides of equation)

Subtraction Property of Equality

If a = b, then a - c = b - c (subtract the same thing from both sides of the equation)

Multiplication Property of Equality

If a = b, then ac = bc (multiply the same thing to both sides of equation)

Division Property of Equality

if a = b, then a/c = b/c, c≠0 (divide the same thing to both sides of the equation)

supplementary angles

Two angles whose sum is 180 degrees

complementary angles

Two angles whose sum is 90 degrees

acute angle

an angle that measures less than 90 degrees

obtuse angle

An angle that measures more than 90 degrees but less than 180 degrees

straight angle

an angle that measures exactly 180 degrees

adjacent angles

Angles that have a common side and a common vertex (corner point).

distance formula

used to find the length between two points

midpoint formula

used to find the point midway between two other points

midpoint

A point that divides a segment into two congruent segments

Reflexive Property

A quantity is congruent (equal) to itself. a = a

Transitive Property

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

two-column proof

A style of proof in which the statements are written in the left-hand column and the reasons are written in the right-hand column.

congruent symbol

Having the same measure

inductive reasoning

A type of logic in which generalizations are based on specific examples or observations.

deductive reasoning

Uses a sequence of logical statements to prove a conclusion through the use of properties and definitions.