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Glossary
A
acute angle
(p. 28) An angle with measure between 0° and
90°.
angle bisector (p. 36) A ray that divides an angle into two
adjacent angles that are congruent.
acute triangle (p. 194) A triangle with three acute angles.
adjacent angles (p. 28) Two angles with a common vertex
A
and side but no common interior points.
adjacent sides of a triangle
D
C
(p. 195) Two sides of a triangle
with a common vertex.
alternate exterior angles
B
˘
CD bisects ™ACB.
m™ACD = m™BCD
(p. 131) Two angles that are
formed by two lines and a transversal and that lie outside
the two lines on opposite sides of the transversal. See angles
1 and 8.
t
angle bisector of a triangle
(p. 274) A bisector of an angle
1
of the triangle.
8
angle of elevation (p. 561) When you stand and look up at a
point in the distance, the angle that your line of sight makes
with a line drawn horizontally.
angle of depression
alternate interior angles
(p. 131) Two angles that are
formed by two lines and a transversal and that lie between
the two lines on opposite sides of the transversal. See angles
3 and 6.
B
A
angle of elevation
t
angle of rotation
(p. 412) The angle formed when rays are
drawn from the center of rotation to a point and its image.
See also rotation.
3
6
apothem of a polygon
(p. 670) The distance from the center
of a polygon to any side of the polygon.
altitude of a triangle
(p. 281) The perpendicular segment
from a vertex of a triangle to the opposite side or to the line
that contains the opposite side.
A
A
A
arc length (p. 683) A portion of the circumference of a circle.
axioms (p. 17) See postulates.
B
base of an isosceles triangle
(p. 195) The noncongruent side
of an isosceles triangle that has only two congruent sides.
D
angle
D
D
Æ
Altitude AD , inside, on, and outside a triangle
(p. 26) Consists of two different rays that have the same
initial point. The rays are the sides of the angle, and the initial
point is the vertex of the angle. The angle symbol is ™.
vertex
sides
B
™BAC, ™CAB, or ™A
876
Student Resources
leg
leg
base
angles
base
C
A
vertex angle
bases of a prism (p. 728) See prism.
bases of a trapezoid (p. 356) See trapezoid.
base angles of an isosceles triangle (p. 236) The two angles
that contain the base of an isosceles triangle. See also base of
an isosceles triangle.
base angles of a trapezoid (p. 356) Two pairs of angles
whose common side is the base of a trapezoid.
base
A
chord of a sphere
(p. 759) A segment whose endpoints are
on the sphere.
circle
(p. 595) The set of all points in a plane that are
equidistant from a given point, called the center of the circle.
B
base angles
P
D
C
base
Circle with center P, or ›P
™A and ™B are a pair of base angles.
™C and ™D are another pair.
circular cone
between
(p. 18) When three points lie on a line, you can say
that one of them is between the other two.
A
C
B
Point B is between points A and C.
biconditional statement
(p. 737) A solid with a circular base and a
vertex that is not in the same plane as the base. The lateral
surface consists of all segments that connect the vertex with
points on the edge of the base. The altitude, or height, is the
perpendicular distance between the vertex and the plane that
contains the base.
vertex
height
(pp. 80, 87) A statement that
slant
height
contains the phrase “if and only if.” The symbol for “if and
only if” is ¯
˘.
bisect
(pp. 34, 36) To divide into two congruent parts.
border pattern
(p. 437) See frieze pattern.
C
r
base
lateral
surface
circumcenter of a triangle
center of a circle
(p. 273) The point of
concurrency of the perpendicular bisectors of a triangle.
(p. 595) See circle.
center of a polygon
(p. 670) The center of its circumscribed
circle.
center of a sphere
(p. 759) See sphere.
center of rotation (p. 412) See rotation.
central angle of a circle (p. 603) An angle whose vertex is
the center of a circle.
P
circumference (p. 683) The distance around a circle.
circumscribed circle (p. 615) A circle with an inscribed
polygon. See also inscribed polygon.
collinear points
(p. 10) Points that lie on the same line.
common tangent (p. 596) A line or segment that is tangent to
two circles. A common internal tangent intersects the segment
that joins the centers of the two circles. A common external
tangent does not intersect the segment that joins the centers of
the two circles.
C
m
q
™PCœ is a central angle.
A
central angle of a regular polygon
k
B
(p. 671) An angle whose
vertex is the center of the polygon and whose sides contain
two consecutive vertices of the polygon.
centroid of a triangle
Line m is a common internal tangent.
Line k is a common external tangent.
(p. 279) The point of concurrency of
the medians of a triangle.
chord of a circle
(p. 595) A segment whose endpoints are
points on the circle.
q
P
(p. 34) A construction tool used to draw arcs.
complement
(p. 46) The sum of the measures of an angle and
its complement is 90°.
T
S
compass
R
complementary angles
(p. 46) Two angles whose measures
have the sum 90°.
Æ Æ
Chords: œR , ST
Glossary
877
component form
(p. 423) The form of a vector that combines
the horizontal and vertical components of the vector.
œ
3 units
up
P
5 units
to the right
construct
(p. 34) To draw using a limited set of tools, usually
a compass and a straightedge.
construction
(p. 34) A geometric drawing that uses a limited
set of tools, usually a compass and a straightedge.
contrapositive (p. 72) The statement formed when you
negate the hypothesis and conclusion of the converse of a
conditional statement.
converse
¤ with component form 具5, 3典
Pœ
composition of transformations
(p. 431) The result when
two or more transformations are combined to produce a single
transformation. An example is a glide reflection.
(p. 72) The statement formed by switching the
hypothesis and conclusion of a conditional statement.
convex polygon (p. 323) A polygon such that no line
containing a side of the polygon contains a point in the
interior of the polygon. A polygon that is not convex is
nonconvex, or concave.
concave polygon (p. 323) See convex polygon.
concentric circles (p. 596) Circles that have a common
interior
center.
interior
convex polygon
concave polygon
convex polyhedron
the same point.
(p. 720) A polyhedron such that any two
points on its surface can be connected by a line segment that
lies entirely inside or on the polyhedron. If this line goes
outside the polyhedron, then the polyhedron is nonconvex, or
concave.
conditional statement
(p. 71) A type of logical statement
that has two parts, a hypothesis and a conclusion.
coordinate
cone
coordinate proof
conclusion (p. 71) The “then” part of a conditional statement.
concurrent lines (p. 272) Three or more lines that intersect in
(p. 737) See circular cone.
congruent angles (p. 26) Angles that have the same measure.
congruent arcs (p. 604) Two arcs of the same circle or of
(p. 17) The real number that corresponds to a
point on a line.
(p. 243) A type of proof that involves
placing geometric figures in a coordinate plane.
congruent circles that have the same measure.
coplanar points (p. 10) Points that lie on the same plane.
corollary (p. 197) A statement that can be proved easily using
congruent circles
(p. 595) Two circles that have the same
a theorem or a definition.
(p. 202) Two geometric figures that have
corresponding angles (p. 131) Two angles that are formed
by two lines and a transversal and occupy corresponding
positions. See angles 1 and 5.
radius.
congruent figures
exactly the same size and shape. When two figures are
congruent, all pairs of corresponding angles and
corresponding sides are congruent. The symbol for “is
congruent to” is £.
congruent segments
t
1
(p. 19) Segments that have the same
length.
5
conjecture
(p. 4) An unproven statement that is based on
observations.
consecutive interior angles
(p. 131) Two angles that are
formed by two lines and a transversal and that lie between the
two lines on the same side of the transversal. Also called same
side interior angles. See angles 3 and 5.
t
3
5
878
Student Resources
corresponding angles of congruent figures
(p. 202) When
two figures are congruent, the angles that are in
corresponding positions and are congruent.
corresponding sides of congruent figures
(p. 202) When
two figures are congruent, the sides that are in corresponding
positions and are congruent.
cosine (p. 558) A trigonometric ratio, abbreviated as cos.
For right triangle ABC, the cosine of the acute angle A is
B
side adjacent to ™A
cos A = ᎏᎏᎏ
hypotenuse
hypotenuse
c
b
c
= ᎏᎏ
diameter of a sphere
(p. 759) A chord that contains the
center of the sphere. The length of a chord that contains the
center of the sphere.
side
a opposite
⬔A
A
b
C
side adjacent to ⬔A
counterexample
(p. 4) An example that shows a conjecture
is false.
dilation
cross section
(p. 720) The intersection of a plane and a solid.
sphere
plane
(p. 506) A type of transformation, with center C and
scale factor k, that maps every point P in the plane to a point
P§ so that the following two properties are true. (1) If P is not
Æ˘
the center point C, then the image point P§ lies on CP . The
scale factor k is a positive number such that CP§ = k(CP),
and k ≠ 1. (2) If P is the center point C, then P = P§.
P’
cylinder
2
P
(p. 730) A solid with congruent circular bases that lie
1
C
in parallel planes. The altitude, or height, of a cylinder is the
perpendicular distance between its bases. The radius of the
base is also called the radius of the cylinder.
base
Dilation with k = 2
radius r
direction of a vector
height h
base
(p. 574) Determined by the angle that
the vector makes with a horizontal line.
distance between two points on a line
(p. 17) The absolute
value of the difference between the coordinates of the points.
The distance between A and B is written as AB, which is also
Æ
called the length of AB .
A
x1
D
AB =|x2 ºx1|
definition (p. 10) Uses known words to describe a new word.
diagonal of a polygon (p. 324) A segment that joins two
nonconsecutive vertices of a polygon.
Distance Formula
q
R
S
P
diagonals
T
diameter of a circle
B
x2
AB
(p. 19) If A(x1, y1) and B(x2, y2) are
points in a coordinate plane, then the distance between A and
B is
2
2
(x苶
º苶x苶
+苶( 苶
y2苶
º苶y苶
AB = 兹苶
2苶
1)苶苶
1)苶.
distance from a point to a line (p. 266) The length of the
perpendicular segment from the point to the line.
q
(p. 595) A chord that passes through the
center of the circle. The distance across a circle, through its
center.
q
P
m
P
The distance from
œ to m is œP.
R
Æ
Diameter: œR or œR
dodecahedron
(p. 721) A polyhedron with twelve faces.
Glossary
879
EF
edge
GF
(p. 719) A line segment formed by the intersection of
two faces of a polyhedron. See also polyhedron.
endpoints (p. 11) See line segment.
enlargement (p. 506) A dilation with k > 1.
equal vectors
(p. 574) Two vectors that have the same
magnitude and direction.
equiangular polygon
(p. 323) A polygon with all of its
interior angles congruent.
equiangular triangle
geometric mean
a
x
geometric probability
(p. 699) A probability that involves a
geometric measure such as length or area.
glide reflection
(p. 430) A transformation in which every
point P is mapped onto a point Pfl by the following two steps.
(1) A translation maps P onto P§. (2) A reflection in a line k
parallel to the direction of the translation maps P§ onto Pfl.
(p. 194) A triangle with three
P’
œ’
(p. 266) The same distance from
one line as from another line.
equidistant from two points
P
(p. 264) The same distance
from one point as from another point.
equilateral polygon
x
b
the positive number x such that ᎏᎏ = ᎏᎏ, or x = 兹a苶苶•苶.
b
congruent angles.
equidistant from two lines
(p. 466) For two positive numbers a and b,
k
œ
œ ’’
(p. 323) A polygon with all of its sides
congruent.
equilateral triangle
(p. 194) A triangle with three congruent
P ’’
sides.
equivalent statements
(p. 72) Two statements that are both
true or both false.
great circle
(p. 760) The intersection of a sphere and a plane
that contains the center of the sphere.
exterior of an angle
(p. 27) All points not on the angle or in
its interior. See also interior of an angle.
exterior of a circle
(p. 596) All points of the plane that are
outside a circle.
exterior angles of a triangle
(p. 196) When the sides of a
triangle are extended, the angles that are adjacent to the
interior angles.
B
great circle
HF
hemisphere
(p. 760) Half of a sphere, formed when a great
circle separates a sphere into two congruent halves.
A
C
exterior angles
hypotenuse (p. 195) In a right triangle, the side opposite the
right angle. See also legs of a right triangle.
hypothesis
external segment
(p. 630) The part of a secant segment that
is not inside the circle.
extremes of a proportion
(p. 459) The first and last terms of
a
b
c
d
a proportion. The extremes of ᎏᎏ = ᎏᎏ are a and d.
FF
face
IF
icosahedron
if-then form
(p. 721) A polyhedron with twenty faces.
(p. 71) The form of a conditional statement that
uses the words “if” and “then.” The “if” part contains the
hypothesis and the “then” part contains the conclusion.
image
(p. 719) See polyhedron.
flow proof
(pp. 135, 136) A type of proof that uses arrows to
show the flow of a logical argument. Statements are
connected by arrows to show how each statement comes from
the ones before it, and each reason is written below the
statement it justifies.
frieze pattern
(p. 437) A pattern that extends to the left and
right in such a way that the pattern can be mapped onto itself
by a horizontal translation. Also called border pattern.
880
(p. 71) The “if” part of a conditional statement.
Student Resources
(p. 396) The new figure that results from the
transformation of a figure in a plane. See also preimage.
incenter of a triangle
(p. 274) The point of concurrency of
the angle bisectors of a triangle.
indirect proof (p. 302) A proof in which you prove that a
statement is true by first assuming that its opposite is true. If
this assumption leads to an impossibility, then you have
proved that the original statement is true.
inductive reasoning (p. 4) A process that includes looking
for patterns and making conjectures.
initial point of a ray
KF
(p. 11) See ray.
initial point of a vector
(p. 423) The starting point of a
vector. See also vector.
inscribed angle
(p. 613) An angle whose vertex is on a circle
and whose sides contain chords of the circle.
inscribed
angle
intercepted
arc
kite
(p. 358) A quadrilateral that has two pairs of consecutive
congruent sides, but in which opposite sides are not
congruent.
LF
lateral area of a cylinder
(p. 730) The area of the curved
surface of a cylinder.
inscribed polygon
(p. 615) A polygon whose vertices all lie
on a circle.
lateral area of a polyhedron
(p. 728) The sum of the areas
of the lateral faces of a polyhedron.
lateral faces of a prism (p. 728) See prism.
lateral surface of a cone (p. 737) See circular cone.
Law of Detachment (p. 89) If p ˘ q is a true conditional
statement and p is true, then q is true.
intercepted arc
(p. 613) The arc that lies in the interior of an
inscribed angle and has endpoints on the angle. See also
inscribed angle.
interior of a circle
(p. 596) All points of the plane that are
Law of Syllogism (pp. 89, 90) If p ˘ q and q ˘ r are true
conditional statements, then p ˘ r is true.
legs of an isosceles triangle
(p. 195) The two congruent
sides of an isosceles triangle that has only two congruent
sides. See also base of an isosceles triangle.
inside a circle.
legs of a right triangle
interior of an angle
that form the right angle.
(p. 27) All points between the points
that lie on each side of the angle.
(p. 195) In a right triangle, the sides
hypotenuse
leg
exterior
E
D
leg
interior
A
interior angles of a triangle (p. 196) When the sides of a
triangle are extended, the three original angles of the triangle.
intersect (p. 12) To have one or more points in common.
intersection (p. 12) The set of points that two or more
geometric figures have in common.
inverse
(p. 72) The statement formed when you negate the
hypothesis and conclusion of a conditional statement.
isometry
legs of a trapezoid (p. 356) See trapezoid.
length of a segment (p. 17) The distance between the
endpoints of a segment. See also distance between two points
on a line.
line
(pp. 10, 11) A line extends in one dimension. It is usually
represented by a straight line with two arrowheads to indicate
that the line extends without end in two directions. In this
book, lines are always straight lines. See also undefined term.
A
(p. 397) A transformation that preserves lengths.
l
¯
˘
Also called rigid transformation.
isosceles trapezoid
B
Line l or AB
(p. 356) A trapezoid with congruent legs.
linear pair (p. 44) Two adjacent angles whose noncommon
sides are opposite rays.
5
isosceles triangle
congruent sides.
(p. 194) A triangle with at least two
6
™5 and ™6 are a linear pair.
line of reflection
(p. 404) See reflection.
Glossary
881
line of symmetry (p. 406) A line that a figure in the plane
has if the figure can be mapped onto itself by a reflection in
the line.
measure of an angle (p. 27) Consider a point A on one side
¯
˘
Æ˘
of OB The rays of the form OA can be matched one to one
with the real numbers from 0 to 180. The measure of ™AOB
is equal to the absolute value of the difference between the
Æ˘
Æ˘
real numbers for OA and OB .
0 10
20
180 170 1
3
60 1 0
50 40
14
0
Hexagon with six
lines of symmetry
Hexagon with one
line of symmetry
A
1
line perpendicular to a plane
2
3
(p. 79) A line that intersects
the plane in a point and is perpendicular to every line in the
plane that intersects it.
n
4
70 180
60 1
0 1 0 10 0
15
2
0
0
14 0 3
4
80 90 100 11
01
70
80 7
60 110 100
0 6 20 1
0
3
0
0
2
1
5 0
50 0
13
5
O
6
B
measure of a major arc
(p. 603) The difference between
360° and the measure of its associated minor arc.
measure of a minor arc
(p. 603) The measure of its central
angle.
P
median of a triangle (p. 279) A segment whose endpoints are
a vertex of the triangle and the midpoint of the opposite side.
median
line segment
(p. 11) Part of a line that consists of two points,
called endpoints, and all points on the line that are between
the endpoints. Also called segment.
A
B
AB with endpoints A and B
Æ
midpoint (p. 34) The point that divides, or bisects, a segment
into two congruent segments.
A
M
Æ
M is the midpoint of AB .
locus (p. 642) The set of all points that satisfy a given
condition or a set of given conditions. Plural is loci.
Midpoint Formula
logical argument (p. 89) An argument based on deductive
reasoning, which uses facts, definitions, and accepted
properties in a logical order.
1
1
ᎏ2 , ᎏ
ᎏ2 .
coordinates ᎏ
MF
B
(p. 35) If A(x1, y1) and B(x2, y2) are
Æ
points in a coordinate plane, then the midpoint of AB has
冉
x +x
2
y +y
2
冊
midsegment of a trapezoid
(p. 357) A segment that
connects the midpoints of the legs of a trapezoid.
magnitude of a vector
(p. 573) The distance from the initial
Æ„
point to the terminal point of a vector. The magnitude of AB
Æ„
is the distance from A to B and is written|AB |.
midsegment
major arc
(p. 603) Part of a circle that measures between
180° and 360°. See also minor arc.
A
major
arc
ACB
(p. 287) A segment that connects
the midpoints of two sides of a triangle.
minor
arc
P
AB
C
means of a proportion
midsegment
B
(p. 459) The middle terms of a
c
a
proportion. The means of ᎏᎏ = ᎏᎏ are b and c.
d
b
882
midsegment of a triangle
Student Resources
minor arc
(p. 603) Part of a circle that measures less than
180°. See also major arc.
N
negation
(pp. 72, 88) The negative of a statement. The
parallelogram (p. 330) A quadrilateral with both pairs of
opposite sides parallel. The parallelogram symbol is ⁄.
q
negation symbol is ~.
R
net (p. 729) A two-dimensional representation of all the faces
of a polyhedron.
P
B
⁄PœRS
parallel planes
(p. 129) Two planes that do not intersect.
U
h
W
P
B
nonconvex polygon
S
(p. 323) See convex polygon.
U ∞W
O
oblique prism
(p. 728) A prism whose lateral edges are not
perpendicular to the bases. The length of the oblique lateral
edges is the slant height of the prism.
base
parallel vectors
(p. 574) Two vectors that have the same or
opposite directions.
perpendicular bisector
(p. 264) A segment, ray, line, or
plane that is perpendicular to a segment at its midpoint.
k
slant
height
height
base
Oblique triangular prism
obtuse angle
(p. 28) An angle with measure between 90° and
180°.
obtuse triangle (p. 194) A triangle with one obtuse angle.
octahedron (p. 721) A polyhedron with eight faces.
Æ
˘
opposite rays (p. 11) If C is between A and B, then CA and
A
B
Æ
Line k is a fi bisector of AB .
perpendicular bisector of a triangle
(p. 272) A line, ray, or
segment that is perpendicular to a side of a triangle at the
midpoint of the side.
perpendicular lines
(p. 79) Two lines that intersect to form
a right angle. The symbol for “is perpendicular to” is fi.
n
Æ˘
CB are opposite rays.
A
C
orthocenter of a triangle
B
m
(p. 281) The point of concurrency
of the lines containing the altitudes of a triangle.
P
paragraph proof
(p. 102) A type of proof written in
paragraph form.
parallel lines (p. 129) Two lines that are coplanar and do not
intersect. The symbol for “is parallel to” is ∞.
plane (p. 10) A plane extends in two dimensions. It is usually
represented by a shape that looks like a tabletop or wall. You
must imagine that the plane extends without end, even though
the drawing of a plane appears to have edges. See also
undefined term.
M
A
P
m
n
m ∞n
C
B
Plane M or plane ABC
Glossary
883
Platonic solids
(p. 721) Five regular polyhedra, named after
the Greek mathematician and philosopher Plato, including a
regular tetrahedron, a cube, a regular octahedron, a regular
dodecahedron, and a regular icosahedron.
point
(p. 10) A point has no dimension. It is usually
represented by a small dot. See also undefined term.
pyramid
(p. 735) A polyhedron in which the base is a
polygon and the lateral faces are triangles with a common
vertex. The intersection of two lateral faces is a lateral edge.
The intersection of the base and a lateral face is a base edge.
The altitude, or height, is the perpendicular distance between
the base and the vertex.
vertex
A
point of concurrency
(p. 272) The point of intersection of
lateral edge
height
concurrent lines.
point of tangency (p. 597) See tangent line.
polygon (p. 322) A plane figure that meets the following two
conditions. (1) It is formed by three or more segments called
sides, such that no two sides with a common endpoint are
collinear. (2) Each side intersects exactly two other sides, one
at each endpoint. See also vertex of a polygon.
polyhedron
(p. 719) A solid that is bounded by polygons,
called faces, that enclose a single region of space. Plural is
polyhedra, or polyhedrons.
lateral faces
base
base
edge
Pythagorean triple (p. 536) A set of three positive integers
a, b, and c that satisfy the equation c2 = a2 + b2.
R
radius of a circle
(p. 595) The distance from the center of a
circle to a point on the circle. A segment whose endpoints are
the center of the circle and a point on the circle. Plural is radii.
face
q
P
Æ
Radius: Pœ or Pœ
vertex
postulates
edge
(p. 17) Rules that are accepted without proof. Also
called axioms.
preimage
radius of a polygon
(p. 670) The radius of its circumscribed
circle.
radius of a sphere
(p. 396) The original figure in the transformation of
a figure in a plane. See also image.
(p. 759) A segment from the center of a
sphere to a point on the sphere. The length of a segment from
the center of a sphere to a point on the sphere.
prism
(p. 728) A polyhedron with two congruent faces, called
bases, that lie in parallel planes. The other faces, called
lateral faces, are parallelograms formed by connecting the
corresponding vertices of the bases. The segments connecting
the vertices are lateral edges. The altitude, or height, of a
prism is the perpendicular distance between its bases.
base
lateral
edges
height
lateral
faces
ratio of a to b (p. 457) The quotient ᎏabᎏ if a and b are two
quantities that are measured in the same units. Can also be
written as a :b.
ray
(p. 11) Part of a line that consists of a point, called an
initial point, and all points on the line that extend in one
direction.
base
Right rectangular prism
A
B
˘
AB with initial point A
probability
(p. 699) A ratio from 0 to 1 that represents the
likelihood an event will occur.
proportion
(p. 459) An equation that equates two ratios.
c
a
Example: ᎏᎏ = ᎏᎏ
d
b
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Student Resources
rectangle
(p. 347) A parallelogram with four right angles.
reduction
(p. 506) A dilation with 0 < k < 1.
reflection
(p. 404) A type of transformation that uses a line
that acts like a mirror, called the line of reflection, with an
image reflected in the line.
m
rotational symmetry
(p. 415) A figure in the plane has
rotational symmetry if the figure can be mapped onto itself by
a rotation of 180° or less.
S
same side interior angles
(p. 131) See consecutive interior
angles.
scale factor (p. 474) The ratio of the lengths of two
corresponding sides of two similar polygons.
Line m is a line of reflection.
regular polygon
(p. 323) A polygon that is equilateral and
scalene triangle (p. 194) A triangle with no congruent sides.
secant line (p. 595) A line that intersects a circle in two
points.
equiangular.
m
regular polyhedron
(p. 720) A polyhedron whose faces are
P
all congruent regular polygons.
regular pyramid
(p. 735) A pyramid such that the base is a
regular polygon and the segment from the vertex to the center
of the base is perpendicular to the base. In a regular pyramid,
the lateral faces all have the same slant height.
height
slant
height
Line m is a secant.
secant segment
(p. 630) A segment that intersects a circle in
two points, with one point as an endpoint of the segment.
sector of a circle
(p. 692) The region bounded by two radii of
a circle and their intercepted arc.
A
P
B
rhombus
Sector APB
(p. 347) A parallelogram with four congruent sides.
segment
(p. 11) See line segment.
segment bisector
(p. 34) A segment, ray, line, or plane that
intersects a segment at its midpoint.
right angle
C
(p. 28) An angle with measure equal to 90°.
M
right cone
(p. 737) A cone with a vertex that lies directly
above the center of the base. The slant height of a right cone
is the distance between the vertex and a point on the edge of
the base. See also circular cone.
right cylinder
(p. 730) A cylinder such that the segment
joining the centers of the bases is perpendicular to the bases.
right prism
(p. 728) A prism whose lateral edges are
perpendicular to both bases. See also prism.
right triangle (p. 194) A triangle with one right angle.
rotation (p. 412) A type of transformation in which a figure is
turned about a fixed point, called the center of rotation.
A
¯
˘
center of rotation
Æ
CD is a bisector of AB .
semicircle (p. 603) An arc whose endpoints are the endpoints
of a diameter of the circle.
side opposite a vertex of a triangle
(p. 195) A side of a
triangle that does not contain the given vertex.
sides of an angle
similar polygons
(p. 26) See angle.
(p. 473) Two polygons such that their
corresponding angles are congruent and the lengths of
corresponding sides are proportional. The symbol for “is
similar to” is ~.
B
angle of rotation
B
D
E
A
C
Similar triangles
D
F
Glossary
885
similar solids (p. 766) Two solids with equal ratios of
corresponding linear measures, such as heights or radii.
straight angle
straightedge
(p. 28) An angle with measure equal to 180°.
(p. 34) A construction tool used to draw
segments. A ruler without marks.
sum of two vectors
Æv„
= 具a2, b2典 is
supplement
uƄ
+ Æv„
Æ„ = 具a , b 典 and
(p. 575) The sum of u
1 1
= 具a1 + a2, b1 + b2典.
(p. 46) The sum of the measures of an angle and
its supplement is 180°.
Similar pyramids
supplementary angles
sine (p. 558) A trigonometric ratio, abbreviated as sin.
For right triangle ABC, the sine of the acute angle A is
side opposite ™A
B
sin A = ᎏᎏ
hypotenuse
hypotenuse
c
a
c
= ᎏᎏ
side
a opposite
⬔A
A
b
C
side adjacent to ⬔A
skew lines
(p. 129) Two lines that do not intersect and are
not coplanar.
(p. 46) Two angles whose measures
have the sum 180°.
surface area of a cylinder (p. 730) The sum of the lateral
area of the cylinder and the areas of the two bases.
surface area of a polyhedron
(p. 728) The sum of the areas
of its faces.
T
tangent (p. 558) A trigonometric ratio, abbreviated as tan.
For right triangle ABC, the tangent of the acute angle A is
side opposite ™A
n
tan A = ᎏᎏᎏ
side adjacent to ™A
m
B
hypotenuse
c
a
b
= ᎏᎏ
œ
Lines m and n are skew lines.
side
a opposite
⬔A
A
b
C
side adjacent to ⬔A
tangent circles
(p. 596) Circles that intersect in one point.
solve a right triangle
(p. 567) Determine the measurements
of all sides and angles of a right triangle.
special right triangles (pp. 550, 551) Right triangles whose
angle measures are 45°-45°-90° or 30°-60°-90°.
sphere
(p. 759) The locus of points in space that are a given
distance from a point, called the center of the sphere.
Internally tangent
Externally tangent
tangent line
(p. 595) A line that intersects a circle in exactly
one point, called the point of tangency.
R
center
C
n
square
(p. 347) A parallelogram with four congruent sides
and four right angles.
Line n is a tangent.
R is the point of tangency.
tangent segment
(p. 630) A segment that is tangent to a
circle at an endpoint.
terminal point of a vector
(p. 423) The ending point of a
vector. See also vector.
standard equation of a circle
(p. 636) A circle with radius
r and center (h, k) has this standard equation:
(x º h)2 + (y º k)2 = r 2.
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Student Resources
tetrahedron (p. 721) A polyhedron with four faces.
theorem (p. 102) A true statement that follows as a result of
other true statements.
transformation (p. 396) The operation that maps, or moves,
a preimage onto an image. Three basic transformations are
reflections, rotations, and translations.
translation
(p. 421) A type of transformation that maps every
two points P and Q in the plane to points P§ and Q§, so that
the following two properties are true. (1) PP§= QQ§.
Æ Æ
Æ
Æ
(2) PP§ ∞ QQ§ or PP§ and QQ§ are collinear.
(p. 10) A word, such as point, line, or plane,
that is not formally defined, although there is general
agreement about what the word means.
V
vector
(p. 423) A quantity that has both direction and
magnitude, and is represented by an arrow drawn between
two points.
P’
P
U
undefined term
œ’
C
œ
transversal (p. 131) A line that intersects two or more
coplanar lines at different points.
B
Æ„
BC with initial point B
and terminal point C
t
1 2
3 4
vertex of an angle (p. 26) See angle.
vertex of a polygon (p. 322) Each endpoint of a side of a
5 6
7 8
polygon. Plural is vertices.
q
Line t is a transversal.
(p. 356) A quadrilateral with exactly one pair of
parallel sides, called bases. The nonparallel sides are legs.
base
D
leg
C
base
side
S
T
B
leg
vertex
P
trapezoid
A
R
vertex
vertex of a polyhedron
(p. 719) A point where three or more
edges of a polyhedron meet. See also polyhedron.
vertex of a triangle
(p. 195) Each of the three points joining
the sides of a triangle. Plural is vertices. See also triangle.
triangle
(p. 194) A figure formed by three segments joining
three noncollinear points, called vertices. The triangle symbol
is ¤.
B
vertex angle of an isosceles triangle
(p. 236) The angle
opposite the base of an isosceles triangle. See also base of an
isosceles triangle.
vertical angles
(p. 44) Two angles whose sides form two
pairs of opposite rays.
A
C
¤ABC with vertices A, B, and C
4
1
3
2
trigonometric ratio
(p. 558) A ratio of the lengths of two
sides of a right triangle. See also sine, cosine, and tangent.
two-column proof (p. 102) A type of proof written as
numbered statements and reasons that show the logical order
of an argument.
™1 and ™3 are vertical angles.
™2 and ™4 are vertical angles.
volume of a solid
(p. 743) The number of cubic units
contained in the interior of a solid.
Glossary
887