Vocabulary Flashcards
collinear
points that lie on the same line
coplaner
figures that are in the same plane
space
set of all points
endpoint
a single point indicating where a line segment or ray ends
intersection
a set of points that figures have in common
opposite rays
collinear rays with the same endpoint that form a line
ray
part of the line that consists of one endpoint and all the points of the line on one side of the line
segment
part of the line that consists of two points called endpoints and all of the points between them
skew
lines that do not lie on the same plane
postulate
Also known as an axiom is an accepted statement or fact
theorem
A conjecture that is proven
Conjecture
A conclusion reached by using inductive reasoning
Undefined terms
There are 3 of them. Point, line, and plane. They are the building blocks for the rest of the subject.
Point
In Euclidean geometry, a point is undefined. You can think of it as a location but it has no size.
Line
In Euclidean geometry, a line is undefined. You can think of it as a straight path that extends in two opposite directions without end and has no thickness. Contains infinitely many points (which means A LOT).
Plane
In Euclidean geometry, a plane is undefined. You can think of a plane as a flat surface that extends without end and has no thickness. It contains infinity many lines.
complementary angles
two angles that add to 90 degrees
supplementary angles
two angles that add to 180 degrees
reason
The justification given in a two-column proof that we write on the right-hand side.
statement
The claims we believe are true. We write these on the left-hand side of the two-column proof.
two-column proof
A convincing argument that uses deductive reason. Statements are written on left-hand side and reasons are written on the right-hand side.
addition property of equality
If a=b, then a + c = b + c
Adding the same thing to both sides of an equation without changing the solutions.
subtraction property of equality
If a=b, than a - c = b - c
Subtracting the same thing to both sides of an equation without changing the solutions.
Multiplication property of equality
if a=b, than ac = bc
Multiplying the same thing to both sides of the equation without changing the solutions.
Division property of equality
If a=b and c isn’t 0, than a / c = b / c.
Dividing the same thing to both sides of the equation without changing the solutions. You can not divide by ZERO.
Substitution property of equality
If a = b, then a can be substituted for b in any expression or equation.
Remember from the summer, this was SIDE to PART!
Transitive property of equality
If a = b and b = c, than a = c.
Remember from the summer, this was SIDE to SIDE!
congruent angles
angles that have the same measure
angle bisector
a ray that divides an angle into two congruent angles
compass
a geometric tool used to draw circles and parts of circles called arcs
arc
a portion of the circumference of a circle
straightedge
a ruler with no markings on it
construction
a geometric figure made with only a straightedge and a compass
perpendicular bisector
a line, segment, or ray that is perpendicular to the segment at its midpoint
midpoint
the point that divides the segment into two congruent segments
linear pair
a pair of adjacent angles whose noncommon sides are opposite rays
angle addition postulate
if B is in the interior of
