Big Ideas Math Geometry Vocabulary Flash Cards

Comprehensive vocabulary flashcards covering key definitions, theorems, postulates, and properties from Big Ideas Math Geometry (Chapters 1 through 11).

acute angle

An angle that has a measure greater than $0^\circ$ and less than $90^\circ$.

adjacent angles

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

angle

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

angle bisector

A ray that divides an angle into two angles that are congruent.

axiom

A rule that is accepted without proof.

between

When three points are collinear, one point is between the other two.

collinear points

Points that lie on the same line.

complementary angles

Two angles whose measures have a sum of $90^\circ$.

congruent angles

Two angles that have the same measure.

congruent segments

Line segments that have the same length.

construction

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

coordinate

A real number that corresponds to a point on a line.

coplanar points

Points that lie in the same plane.

defined terms

Terms that can be described using known words, such as point or line.

distance

The absolute value of the difference of two coordinates on a line.

endpoints

Points that represent the ends of a line segment or ray.

exterior of an angle

The region that contains all the points outside of an angle.

interior of an angle

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

intersection

The set of points two or more geometric figures have in common.

line

A line has one dimension. It is represented by a line with two arrowheads, but it extends without end.

line segment

Consists of two endpoints and all the points between them.

linear pair

Two adjacent angles whose noncommon sides are opposite rays.

measure of an angle

The absolute value of the difference between the real numbers matched with the two rays that form the angle on a protractor.

midpoint

The point that divides a segment into two congruent segments.

obtuse angle

An angle that has a measure greater than $90^\circ$ and less than $180^\circ$.

opposite rays

If point $C$ lies on line $AB$ between $A$ and $B$, then ray $CA$ and ray $CB$ are opposite rays.

plane

A flat surface made up of points that has two dimensions and extends without end, and is represented by a shape that looks like a floor or a wall.

point

A location in space that is represented by a dot and has no dimension.

postulate

A rule that is accepted without proof.

ray

Ray $AB$ is a ray if it consists of the endpoint $A$ and all points on line $AB$ that lie on the same side of $A$ as $B$.

right angle

An angle that has a measure of $90^\circ$.

segment bisector

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

sides of an angle

The rays of an angle.

straight angle

An angle that has a measure of $180^\circ$.

supplementary angles

Two angles whose measures have a sum of $180^\circ$.

undefined terms

Words that do not have formal definitions, but there is agreement about what they mean.

vertex of an angle

The common endpoint of the two rays that form an angle.

vertical angles

Two angles whose sides form two pairs of opposite rays.

biconditional statement

A statement that contains the phrase "if and only if".

conclusion

The "then" part of a conditional statement written in if-then form.

conditional statement

A logical statement that has a hypothesis and a conclusion.

conjecture

An unproven statement that is based on observations.

contrapositive

The statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement.

converse

The statement formed by exchanging the hypothesis and conclusion of a conditional statement.

counterexample

A specific case for which a conjecture is false.

deductive reasoning

A process that uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.

equivalent statements

Two related conditional statements that are both true or both false.

flowchart proof (flow proof)

A type of proof that uses boxes and arrows to show the flow of a logical argument.

hypothesis

The "if" part of a conditional statement written in if-then form.

if-then form

A conditional statement in the form "if $p$, then $q$", where the "if" part contains the hypothesis and the "then" part contains the conclusion.

inductive reasoning

A process that includes looking for patterns and making conjectures.

inverse

The statement formed by negating both the hypothesis and conclusion of a conditional statement.

line perpendicular to a plane

A line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point.

negation

The opposite of a statement.

paragraph proof

A style of proof that presents the statements and reasons as sentences in a paragraph, using words to explain the logical flow of an argument.

perpendicular lines

Two lines that intersect to form a right angle.

proof

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

theorem

A statement that can be proven.

truth table

A table that shows the truth values for a hypothesis, conclusion, and a conditional statement.

truth value

A value that represents whether a statement is true (T) or false (F).

two column proof

A type of proof that has numbered statements and corresponding reasons that show an argument in a logical order.

alternate exterior angles

Two angles that are formed by two lines and a transversal that are outside the two lines and on opposite sides of the transversal.

alternate interior angles

Two angles that are formed by two lines and a transversal that are between the two lines and on opposite sides of the transversal.

consecutive interior angles

Two angles that are formed by two lines and a transversal that lie between the two lines and on the same side of the transversal.

corresponding angles

Two angles that are formed by two lines and a transversal that are in corresponding positions.

directed line segment

A segment that represents moving from point $A$ to point $B$.

distance from a point to a line

The length of the perpendicular segment from the point to the line.

parallel lines

Coplanar lines that do not intersect.

parallel planes

Planes that do not intersect.

perpendicular bisector

A line that is perpendicular to a segment at its midpoint.

skew lines

Lines that do not intersect and are not coplanar.

transversal

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

angle of rotation

The angle that is formed by rays drawn from the center of rotation to a point and its image.

center of dilation

The fixed point in a dilation.

center of rotation

The fixed point in a rotation.

center of symmetry

The center of rotation in a figure that has rotational symmetry.

component form

A form of a vector that combines the horizontal and vertical components.

composition of transformations

The combination of two or more transformations to form a single transformation.

congruence transformation

A transformation that preserves length and angle measure.

congruent figures

Geometric figures that have the same size and shape.

dilation

A transformation in which a figure is enlarged or reduced with respect to a fixed point.

enlargement

A dilation in which the scale factor is greater than $1$.

glide reflection

A transformation involving a translation followed by a reflection.

horizontal component

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

image

A figure that results from the transformation of a geometric figure.

initial point

The starting point of a vector.

line of reflection

A line that acts as a mirror for a reflection.

line of symmetry

A line of reflection that maps a figure onto itself.

line symmetry

A figure in the plane has line symmetry when the figure can be mapped onto itself by a reflection in a line.

preimage

The original figure before a transformation.

reduction

A dilation in which the scale factor is greater than $0$ and less than $1$.

reflection

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

rigid motion

A transformation that preserves length and angle measure.

rotation

A transformation in which a figure is turned about a fixed point.

rotational symmetry

A figure has rotational symmetry when the figure can be mapped onto itself by a rotation of $180^\circ$ or less about the center of the figure.

scale factor

The ratio of the lengths of the corresponding sides of the image and the preimage of a dilation.

similar figures

Geometric figures that have the same shape, but not necessarily the same size.

similarity transformation

A dilation or a composition of rigid motions and dilations.

terminal point

The ending point of a vector.

transformation

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