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
