What is a theorem?
Must be proven to be true
What is a postulate?
Accepted to be true without truth
Example of theorem
The angles in a triangle add up to 180 degrees
Example of postulate
A line grows infinitely and is straight
¯AB
The segment of AB
A B →
The ray of AB
What is a line?
Extends in opposite directions without end.
What is a plane?
Extends in two dimensions without end.
What is a ray?
Consists of an endpoint and all points of a line on one side of the endpoint.
What is a coplanar?
Points that lie on the same plane
How can you name a plane?
By using any collinear points
How can you name segments on a line?
By starting from the left to the right; AC, CD, BD, BC
What does collinear mean?
points that lie on the same line
What is a point?
A location
When naming a line or plane make sure the letter is
Italicized/In Cursive
What are parallel lines
lines that never intersect
What is a coinciding line?
Lines that lie upon each other in such a way that when we look at them, they appear to be a single line, instead of double or multiple lines.
Two lines intersect at a
point
Two lines planes at a
line
What are line segments?
Consists of two endpoints and all the points between them
What are opposite rays?
two rays that share the same endpoint and form a line. You start at the middle point and go left and go right/ opposite directions: BA, BC
What is the symbol for congruent?
≅
What is a midpoint?
A point that divides a segment into two congruent segments
If two segments are congruent, then their lengths are
equal
What does bisect mean?
to divide into two equal parts
What is bisector?
a line, segment, ray, or plane that intersects the segment at its midpoint
Two points determine a line
always
The midpoint of a line segment is halfway between the endpoints
always
theorems can be proven using undefined terms, defined terms, postulates, and other theorems
always
Collinear points are on the same line
always
a segment bisector divides a segment into two equal lengths
always
Two lines that intersect lie in exactly in one plane
always
Two lines in two points
never
Congruent segments have different measures
never
Two lines that are parallel intersect in a point
never
Coinciding lines intersect in exactly one point
never
postulates use undefined terms
sometimes
Three points determine a plane
sometimes
two planes intersect in exactly one line
sometimes
coplanar points are on the same line
sometimes
Two planes are parallel
sometimes
two lines and a point lie in the same plane
sometimes
Three planes intersect in three lines
sometimes