Geometry- Chapters 1-12: Vocabulary

diameter (ch 10)

A chord that contains the center of a circle

if-then form(ch 2)

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

line symmetry(ch 4)

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

image(ch 4)

A figure that results from the transformation of a geometric figure

face (ch 12)

A flat or curved surface of a solid

plane(ch 1)

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

component form(ch 4)

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

construction(ch 1)

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

line(ch 1)

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

tangent of a circle (ch 10)

A line in the plane of a circle that intersects the circle at exactly one point

line of symmetry(ch 4)

A line of reflection that maps a figure onto itself.

edge (ch 12)

A line segment or curve formed by the intersection of two faces of a solid

line of reflection(ch 4)

A line that acts as a mirror for a reflection

secant (ch 10)

A line that intersects a circle in two points

perpendicular bisector(ch 3)

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

point(ch 1)

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

proof(ch 2)

A logical argument that shows a statement is true.

population density (ch 11)

A measure of how many people live within a given area

corresponding parts(ch 5)

A pair of sides or angles that have the same relative position in two congruent figures

rhombus (ch 7)

A parallelogram with four congruent sides

square(ch 7)

A parallelogram with four congruent sides and four right angles.

rectangle(ch 7)

A parallelogram with four right angles

vertex of a polyhedron (ch 12)

A point of a polyhedron where three or more edges meet

inscribed polygon (ch 10)

A polygon in which all of the vertices lie on a circle

inductive reasoning(ch 2)

A process that includes looking for patterns and making conjectures.

deductive reasoning(ch 2)

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

trapezoid

A quadrilateral with at least one pair of parallel sides

Trigonometric Ratio (ch 9)

A ratio of the lengths of two sides in a right triangle.

secant segment (ch 10)

A segment that contains a chord of a circle, and has exactly one endpoint outside the circle

tangent segment (ch 10)

A segment that is tangent to a circle at an endpoint

diagonal(ch 7)

A segment that joins two nonconsecutive vertices of a polygon

chord of a sphere (ch 12)

A segment whose endpoints are on a sphere

radius of a circle (ch 10)

A segment whose endpoints are the center and any point on a circle

angle(ch 1)

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

biconditional statement(ch 2)

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

paragraph proof(ch 2)

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

truth table(ch 2)

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

solid of revolution (ch 12)

A three-dimensional figure that is formed by rotating a two-dimensional shape around an axis

dilation(ch 4)

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

rotation(ch 4)

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

translation(ch 4)

A transformation that moves every point of a figure the same distance in the same direction

flowchart proof (flow proof)(ch 2)

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

radian (ch 11)

A unit of measurement for angles

truth value(ch 2)

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

ray(ch 1)

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

central angle of a regular polygon (ch 11)

An angle formed by two radii drawn to consecutive vertices of a polygon

obtuse angle(ch 1)

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

central angle of a circle (ch 10)

An angle whose vertex is the center of a circle

inscribed angle (ch 10)

An angle whose vertex lies on a circle and whose sides contain chords of the circle

major arc (ch 10)

An arc of a circle whose measure is greater than 180 degrees.

minor arc (ch 10)

An arc of a circle whose measure is less than 180 degrees.

intercepted arc (ch 10)

An arc that lies between two lines, rays, or segments

semicircle (ch 10)

An arc with endpoints that are the endpoints of a diameter

inverse sine (ch 9)

An inverse trigonometric ratio abbreviated as sin-1

inverse cosine (ch 9)

An inverse trigonometric ratio, abbreviated as cosˉ¹

adjacent arcs (ch 10)

Arcs of a circle that have exactly one point in common

similar arcs (ch 10)

Arcs that have the same measure

congruent circles (ch 10)

Circles that can be mapped onto each other by a rigid motion or a composition of rigid motions

lateral area of a cone (ch 12)

Consists of all segments that connect the vertex with points on the base edge of a cone

tangent circles (ch 10)

Coplanar circles that intersect in one point

kite(ch 7)

a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent

vector(ch 4)

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

angle bisector(ch 1)

a ray that divides an angle into two angles that are congruent

postulate(ch 1)

a rule that is accepted as true without proof

axiom(ch 1)

a rule that is accepted without proof

median of a triangle(ch 6)

a segment from a vertex of a triangle to the midpoint of the opposite side

midsegment of a triangle(ch 6)

a segment that connects the midpoints of two sides of a triangle

directed line segment(ch 3)

a segment that represents moving from point A to point B is called the directed line segment AB

chord of a circle (ch 10)

a segment whose endpoints are on a circle

Counterexample(ch 2)

a specific case for which the conjecture is false

corollary to a theorem(ch 5)

a statement that can be proved easily using the theorem

theorem(ch 2)

a statement that can be proven

indirect proof(ch 6)

a style of proof in which you temporarily assume that the desired conclusion is false, then reason logically to a contradiction

coordinate proof(ch 5)

a style of proof that involves placing geometric figures in a coordinate plane

glide reflection(ch 4)

a transformation involving a translation followed by a reflection

congruence transformation(ch 4)

a transformation that preserves length and angle measure

rigid motion(ch 4)

a transformation that preserves length and angle measure ex. translations, reflections, and rotations

reflection(ch 4)

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

isosceles trapezoid(ch 7)

a trapezoid with congruent legs

two-column proof(ch 2)

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

angle of elevation (ch 9)

an angle formed by a horizontal line and the line of sight to an object above the horizontal line

straight angle(ch 1)

an angle that measures 180 degrees

right angle(ch 1)

an angle that measures 90 degrees

acute angle(ch 1)

an angle that measures more than 0 degrees, but less than 90 degrees

circumscribed angle (ch 10)

an angle whose sides are tangent to a circle

inverse tangent (ch 9)

an inverse trigonometric ratio, abbreviated as tan-1

interior angles(ch 5)

angles of a polygon

congruent arcs (ch 10)

arcs that have the same measure and are in the same circle or in congruent circles

line segment(ch 1)

consists of two endpoints and all the points between them

segment(ch 1)

consists of two endpoints and all the points between them

concentric circles (ch 10)

coplanar circles that have the same center

parallel lines(ch 3)

coplanar lines that do not intersect

Base angles of a triangle(ch 7)

either of the angles of a triangle that have one side in common with the base

sine (ch 9)

for an acute angle of a right triangle, the ratio of the length of the leg opposite the acute angle to the length of the hypotenuse

cosine (ch 9)

for an acute angle of a right triangle, the ratio of the measure of the leg adjacent to the acute angle to the measure of the hypotenuse

similar figures(ch 4)

geometric figures that have the same shape but not necessarily the same size

congruent figures(ch 4)

geometric figures that have the same size and shape

parallel planes(ch 3)

planes that do not intersect

collinear points(ch 1)

points that lie on the same line

coplanar points(ch 1)

points that lie on the same plane

congruent segments(ch 1)

segments that have the same length

defined terms(ch 1)

terms that can be described using known words such as point or line

hypothesis(ch 2)

the "if" part of a conditional statement

measure of an angle(ch 1)

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

distance(ch 1)

the absolute value of the difference of the coordinates on a line

vertex angle(ch 5)

the angle formed by the legs of an isoceles triangle

angle of rotation(ch 4)

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

exterior angles(ch 5)

the angles that form linear pairs with the interior angles of a polygon

center of symmetry(ch 4)

the center of rotation in a figure that has rotational symmetry

circumscribed circle (ch 10)

the circle that contains the vertices of an inscribed polygon

terminal point(ch 4)

the ending point of a vector

center of rotation(ch 4)

the fixed point in a rotation

cross section (ch 12)

the intersection of a solid and a plane

distance from a point to a line(ch 3)

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

legs of a trapezoid(ch 7)

the nonparallel sides of a trapezoid

bases of a trapezoid(ch 7)

the parallel sides of a trapezoid

altitude of a triangle(ch 6)`

the perpendicular segment from a vertex of a triangle to the opposite side or to the line that contains the opposite side

incenter(ch 6)

the point of concurrency of the angle bisectors of a triangle

orthocenter(ch 6)

the point of concurrency of the lines containing the altitudes of a triangle

centroid(ch 6)

the point of concurrency of the three medians of a triangle

point of concurrency(ch 6)

the point of intersection of concurrent lines, rays, or segments

midpoint(ch 1)

the point that divides a segment into two congruent segments

circumcenter(ch 6)

the points of concurrency of the three perpendicular bisectors of a triangle

radius of a regular polygon (ch 11)

the radius of a polygon's circumscribed circle

sides of an angle(ch 1)

the rays of an angle

coordinate(ch 1)

the real number that corresponds to a point on a line

interior of an angle(ch 1)

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

exterior of an angle(ch 1)

the region that contains all the points outside of an angle

midsegment of a trapezoid(ch 7)

the segment whose endpoints are the midpoints of the legs of the trapezoid

intersection(ch 1)

the set of points that two or more geometric figures have in common

legs of a right triangle(ch 5)

the sides adjacent to the right angle

base of an isosceles triangle(ch 5)

the sides of an isosceles triangle that is not one of the legs

geometric mean (ch 9)

The positive number x that satisfies a/x = x/b

standard equation of a circle (ch 10)

(x-h)^2 + (y-k)^2 = r^2

Tangent (ch 9)

For an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the leg adjacent to the acute angle.

opposite rays(ch 1)

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

subtend (ch 10)

If the endpoints of a chord or arc lie on the sides of an inscribed angle, the chord or arc is said to subtend the angle.

Cavalieri's Principle (ch 12)

If two solids have the same height and the same cross-sectional area at every level, then they have the same volume.

skew lines(ch 3)

Lines that do not intersect and are not coplanar

endpoints(ch 1)

Points that represent the ends of a line segment or ray

Pythagorean triple (ch 9)

Set of 3 nonzero whole numbers a, b, and c that satisfy the Pythagorean Theorem

conclusion(ch 2)

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

density (ch 12)

The amount of matter that an object has in a given unit of volume

angle of depression(ch 9)

The angle formed by a horizontal line and the line of sight down to an object

center of a regular polygon (ch 11)

The center of a polygon's circumscribed circle

vertex of an angle(ch 1)

The common endpoint of the two rays that form an angle

vertex of a pyramid (ch 12)

The common point of the lateral faces of a pyramid

lateral area of a cylinder (ch 12)

The curved surface of a cylinder

circumference (ch 11)

The distance around a circle

apothem of a regular polygon (ch 11)

The distance from the center to any side of a regular polygon

center of dilation(ch 4)

The fixed point in a dilation

slant height of a regular pyramid (ch 12)

The height of a lateral face of a regular pyramid

horizontal component(ch 4)

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

great circle (ch 12)

The intersection of a plane and a sphere such that the plane contains the center of the sphere

axis of revolution (ch 12)

The line around which a two-dimensional shape is rotated to form a three-dimensional figure

measure of a major arc (ch 10)

The measure of a major arc's central angle

measure of a minor arc (ch 10)

The measure of a minor arc's central angle

volume (ch 12)

The number of cubic units contained in the interior of a solid

negation(ch 2)

The opposite of a statement

lateral area of a polyhedron (ch 12)

The parallelograms formed by connecting the corresponding vertices of the bases

external segment (ch 10)

The part of a secant segment that is outside the circle

point of tangency (ch 10)

The point at which a tangent line intersects a circle

center of a circle (ch 10)

The point from which all points on a circle are equidistant

scale factor(ch 4)

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

sector of a circle (ch 11)

The region bounded by two radii of the circle and their intercepted arc

segments of a chord (ch 10)

The segments formed from two chords that intersect in the interior of a circle

circle (ch 10)

The set of all points in a plane that are equidistant from a given point

hypotenuse(ch 5)

The side opposite the right angle in a right triangle.

surface area of a solid

The sum of the areas of the faces

legs of an isosceles triangle(ch 5)

The two congruent sides of an isosceles triangle are called the legs.

consecutive interior angles(ch 3)

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

complementary angles(ch 1)

Two angles whose sum is 90 degrees

equivalent statements(ch 2)

Two related conditional statements that are both true or both false

polyhedron (ch 12)

Two solids of the same type with equal ratios of corresponding linear measures

similar solids (ch 12)

Two solids of the same type with equal ratios of corresponding linear measures

between(ch 1)

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

undefined terms(ch 1)

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

unit circle (ch 9)

a circle with a radius of 1, centered at the origin

composition of transformations(ch 4)

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

regular polygon(ch 7)

a convex polygon that is both equilateral and equiangular

similarity transformation(ch 4)

a dilation or a composition of rigid motions and dilations

reduction(ch 4)

a dilation with a scale factor between 0 and 1

enlargement(ch 4)

a dilation with a scale factor greater than 1

rotational symmetry(ch 4)

a figure has rotational symmetry when the figure can be mapped onto itself by a rotation of 180° or less about the center of rotation

transformation(ch 4)

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

line perpendicular to a plane(ch 2)

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

transversal(ch 3)

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

common tangent (ch 10)

a line that is tangent to two circles

conditional statement(ch 2)

a logical statement that has a hypothesis and a conclusion

equidistant (ch 6)

a point is equidistant from two figures when it is the same distance from each figure.

segment bisector(ch 1)

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

equiangular polygon(ch 7)

a polygon in which all angles are congruent

equilateral polygon(ch 7)

a polygon in which all sides are congruent

arc length (ch 11)

a portion of the circumference of a circle

Parallelogram(ch 7)

a quadrilateral with both pairs of opposite sides parallel

initial point(ch 4)

the starting point of a vector

converse(ch 2)

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

inverse(ch 2)

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

Contrapositive(ch 2)

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

base angles of an isosceles triangle(ch 5)

the two angles adjacent to the base of an isosceles triangle

vertical component(ch 4)

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

concurrent(ch 6)

three or more lines, rays, or segments that intersect in the same point

linear pair(ch 1)

two adjacent angles whose noncommon sides are opposite rays

alternate interior angles(ch 3)

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

alternate exterior angles(ch 3)

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

corresponding angles(ch 3)

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

congruent angles(ch 1)

two angles that have the same measure

adjacent angles(ch 1)

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

supplementary angles(ch 1)

two angles whose measures have a sum of 180 degrees

vertical angles(ch 1)

two angles whose sides form two pairs of opposite rays

conjecture(ch 2)

unproven statement that is based on observations