Acc Geo Vocab Terms

Line

A line has one dimension and extends without end. Through any two points there is exactly one line.

Plane

A plane has two dimensions. Through any three points not on the same line, there is exactly one plane.

Collinear Points

Points that lie on the same line.

Coplanar Points

Points that lie on the same plane.

Segment

A segment consists of two endpoints and all the points on the line between those points.

Ray

A ray consists of one endpoint and all the points on the same side of a line as any other point on that line.

Opposite Ray

Two rays going in opposite directions that start at the same point on the line and go through two other, separate points.

Intersection

When two or more geometric figures have one or more points in common. The intersection of these figures is the set of points the figures have in common.

Ruler Postulate

The distance between two points on a line is the absolute value of the difference of those two coordinates.

Coordinate

The real number that corresponds to a point.

Distance

(google def)

The amount of space between two points

Construction

A geometric drawing that uses a limited set of tools, usually a compass and a straightedge.

Segment Addition Postulate

If point B is between points A and C, then AB + BC = AC

If AB+BC=AC, then B is between A and C.

Midpoint

the point that divides a segment into two congruent segments

Segment Bisector

a point, ray, line, line segment, or plane that intersects the segment at its midpoint.

Midpoint Formula

Using the coordinates of the two points of which the resulting point is the midpoint of;

( x1+x2/2, y1+y2/2)

Distance Formula

Used to find the distance between two points

Polygon Classification

3 - Triangle

4 - Quadrilateral

5 - Pentagon

6 - Hexagon

7 - Heptagon

8 - Octagon

9 - Nonagon

10 - Decagon

12 - Dodecagon

n - n-gon (ex: 14-gon)

Angle

a set of points consisting of two different rays that have the same endpoint

Vertex

The endpoint where two rays intersect

Interior of an angle

The region that contains all the points between the sides of the angle.

exterior of an angle

The region that contains all the points outside the angle

measure

the absolute value of the difference between the real numbers matched to the vertex of the angle to two points on either side of the angle.

acute

measures greater than 0 and less than 90

right

measures 90

straight angles

measures 180

obtuse

measures greater than 90 and less than 180

angle addition postulate

the measures of two angles that are directly next to each other when added together are equal to the measure of the angle that is created by combining both of them.

complementary angles

two positive angles whose sum is 90

supplementary angles

two positive angles whose sum is 180

adjacent angles

two angles that share a common vertex and a side, but have no common interior points.

linear pairs

two adjacent angles where their common sides are opposite rays. The angles are supplementary angles.

vertical angles

two angles when their sides form two pairs of opposite rays

conditional statement

a logical statement that has two parts, a hypothesis and a conclusion

if-then form

A conditional statement where the if part contains a hypothesis and the then part contains the conclusion.

hypothesis

A testable prediction, often implied by a theory

conclusion

a judgement based on the information obtained

negation

the opposite of the original statement, write ~ before the letter to negate the statement. ex; ~p

converse

to write the converse of a conditional statement exchange the hypothesis and the conclusion.

inverse

to write the inverse of a conditional statement negate both the hypothesis and the conclusion

contrapositive

to write the contrapositive of a conditional statement, first write the converse. Then negate both the hypothesis and the conclusion.

equivalent statements

when two statements are both true or both false.

perpendicular lines

two lines that intersect to form a right angle

biconditional statement

a statement that contains the phrase "if and only if"

truth value

the truth value of a statement is either true or false

truth table**********

used to determine the conditions under which a conditional statement is true by using a truth table.

conjecture

an unproven statement that is based on observations.

inductive reasoning

reasoning used when you find a pattern in specific cases and then write a conjecture for the general case.

counterexample

a specific case for which the conjecture is false

deductive reasoning

reasoning using facts, definitions, accepted properties, and the laws of logic to from a logical argument.

two point postulate

a line contains at least two points

line-point postulate

through any two points there is exactly one line.

line intersection postulate

if two lines intersect, then their intersection is exactly one point

three point postulate

through any three noncollinear points, there exists exactly one plane.

plane-point postulate

a plane contains at least three noncollinear points.

plane-line postulate

If two points lie in a plane, then the line containing them lies in the plane

Plane Intersection Postulate

If two planes intersect, then their intersection is a line.

Addition Property of Equality

If a=b, then a+c=b+c

Subtraction Property of Equality

If a=b, then a-c=b-c

multiplication property of equality

If a = b, then ac = bc, c does not equal 0

Division Property of Equality

if a = b and c is not equal to 0, then a/c = b/c

substitution property of equality

If a=b, then a may be replaced by b in any equation or expression

Distribution Property

sum: a(b+c) = ab+ac

difference: a(b-c) = ab - ac

reflexive property

a = a

symmetric property

if a=b, then b=a

transitive property

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

proof

a logical argument that uses deductive reasoning to show that a statement is true.

congruent supplements theorem

If two angles are supplementary to the same angle (or congruent angles), then they are congruent.

congruent complements theorem

If two angles are complementary to the same angle (or to congruent angles), then they are congruent.

Linear pair postulate

if two angles form a linear pair, then they are supplementary.

vertical angle

vertical angles are congruent

theorem

a statement that can be proven

parallel lines

two lines that do not intersect and are coplanar.

parallel planes

two planes that do not intersect

skew lines

two lines that do not intersect and

transversal

a line that intersects two or more coplanar lines at different points.

corresponding angles

when two angles have corresponding positions.

alternate exterior angles

two angles which lie outside the two lines and on opposite sides of the transversal.

alternate interior angles

two angles which lie between the two lines and on opposite sides of the transversal line.

consecutive interior angles

two angles which lie between the two lines and on the same side of the transversal line.

corresponding angles postulate

if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

alternate interior angles theorem

if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.if two pa

alternate exterior angles theorem

if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

consecutive interior angle theorem

if two lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

corresponding angles postulate converse

if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.

alternate interior angles theorem converse

if two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.

Alternate exterior Angles Theorem converse

If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel.

consecutive interior angle theorem converse

If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.

vector

a quantity that has both direction and magnitude, or size, and is represented in the coordinate plane by an arrow drawn from one point to another.

initial point

the starting point of a vector

terminal point

the ending point of a vector

horizontal component

The horizontal change from the starting point of a vector to the ending point

vertical component

The vertical change from the starting point of a vector to the ending point

component form

combines the horizontal and vertical components of a vector

transformation

a function that moves or changes a figure in some way to produce a new figure called

image

The figure after a transformation

preimage

The original figure

rigid motion

a transformation that preserves length and angle measure

composition of transformations

when two or more transformations are combined to form a single transformation.

reflection

a transformation that uses a line like a mirror to reflect a figure