Download Geometry Glossary acute angle An angle with measure between 0

Geometry Glossary
Adapted from McDougal Littell Geometry
acute angle An angle with measure between 0° and 90°.
acute triangle A triangle with three acute angles.
adjacent angles Two angles with a common vertex and side but no common
interior points.
adjacent sides of a triangle Two sides of a triangle with a common vertex.
alternate exterior angles Two angles that are formed by two lines and a
transversal and that lie outside the two lines on opposite sides of the transversal.
alternate interior angles Two angles that are formed by two lines and a
transversal and that lie between the two lines on opposite sides of the
transversal.
altitude of a triangle The perpendicular segment from a vertex of a triangle to
the opposite side or to the line that contains the opposite side.
angle 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 angle bisector A ray that divides an angle into two adjacent angles that are
congruent.
angle bisector of a triangle A bisector of an angle of the triangle.
angle of elevation 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 rotation The angle formed when rays are drawn from the center of
rotation to a point and its image. See also rotation.
apothem of a polygon The distance from the center of a polygon to any side of
the polygon.
arc length A portion of the circumference of a circle.
base angles of a trapezoid Two pairs of angles whose common side is the
base of a trapezoid.
base angles of an isosceles triangle The two angles that contain the base of
an isosceles triangle. See also base of an isosceles triangle.
base of an isosceles triangle The non-congruent side of an isosceles triangle
that has only two congruent sides.
between When three points lie on a line, you can say that one of them is
between the other two.
biconditional statement A statement that contains the phrase “if and only if.”
The symbol for if and only if is bisect To divide into two congruent parts.
center of a polygon The center of its circumscribed circle.
central angle of a circle An angle whose vertex is the center of a circle.
central angle of a regular polygon An angle whose vertex is the center of the
polygon and whose sides contain two consecutive vertices of the polygon.
centroid of a triangle The point of concurrency of the medians of a triangle.
chord of a circle A segment whose endpoints are points on the circle.
chord of a sphere A segment whose endpoints are on the sphere.
circle The set of all points in a plane that are equidistant from a given point,
called the center of the circle.
circular cone 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.
circumcenter of a triangle The point of concurrency of the perpendicular
bisectors of a triangle.
circumference The distance around a circle.
circumscribed circle A circle with an inscribed polygon. See also inscribed
polygon.
collinear points Points that lie on the same line.
common tangent 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.
compass A construction tool used to draw arcs.
complement The sum of the measures of an angle and its complement is 90°.
complementary angles Two angles whose measures have the sum 90°.
component form The form of a vector that combines the horizontal and vertical
components of the vector.
composition of transformations The result when two or more transformations
are combined to produce a single transformation. An example is a glide
reflection.
conclusion The “then” part of a conditional statement.
concurrent lines Three or more lines that intersect in the same point.
conditional statement A type of logical statement that has two parts, a
hypothesis and a conclusion.
congruent angles Angles that have the same measure.
congruent arcs Two arcs of the same circle or of congruent circles that have
the same measure.
congruent circles Two circles that have the same radius.
congruent figures Two geometric figures that have 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 Segments that have the same length.
conjecture An unproven statement that is based on observations.
consecutive interior angles 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.
construct To draw using a limited set of tools, usually a compass and a
straightedge.
construction A geometric drawing that uses a limited set of tools, usually a
compass and a straightedge.
contrapositive The statement formed when you negate the hypothesis and
conclusion of the converse of a conditional statement.
converse The statement formed by switching the hypothesis and conclusion of
a conditional statement.
convex polygon 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.
convex polyhedron 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.
coordinate The real number that corresponds to a point on a line.
coordinate proof A type of proof that involves placing geometric figures in a
coordinate plane.
coplanar points Points that lie on the same plane.
corollary A statement that can be proved easily using a theorem or a definition.
corresponding angles Two angles that are formed by two lines and a
transversal and occupy corresponding positions.
corresponding angles of congruent figures When two figures are congruent,
the angles that are in corresponding positions and are congruent.
corresponding sides of congruent figures When two figures are congruent,
the sides that are in corresponding positions and are congruent.
cosine A trigonometric ratio, abbreviated as cos. For right triangle ABC, the
cosine of the acute angle A is cos A= (side adjacent to A)/hypotenuse
counterexample An example that shows a conjecture is false.
cross section The intersection of a plane and a solid.
cylinder A solid with congruent circular bases that lie 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.
definition Uses known words to describe a new word.
diagonal of a polygon A segment that joins two nonconsecutive vertices of a
polygon.
diameter of a circle A chord that passes through the center of the circle. The
distance across a circle, through its center.
diameter of a sphere A chord that contains the center of the sphere. The length
of a chord that contains the center of the sphere.
dilation 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 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.
direction of a vector Determined by the angle that the vector makes with a
horizontal line.
distance between two points on a line 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 called the length of AB.
Distance Formula If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then
the distance between A and B is AB= (x2 – x1)2 +(y2 – y1)2.
distance from a point to a line The length of the perpendicular segment from
the point to the line.
dodecahedron A polyhedron with twelve faces.
edge A line segment formed by the intersection of two faces of a polyhedron.
See also polyhedron.
endpoints See line segment.
enlargement A dilation with k > 1.
equal vectors Two vectors that have the same magnitude and direction.
equiangular polygon A polygon with all of its interior angles congruent.
equiangular triangle A triangle with three congruent angles.
equidistant from two lines The same distance from one line as from another
line.
equidistant from two points The same distance from one point as from
another point.
equilateral polygon A polygon with all of its sides congruent.
equilateral triangle A triangle with three congruent sides.
equivalent statements Two statements that are both true or both false.
exterior angles of a triangle When the sides of a triangle are extended, the
angles that are adjacent to the interior angles.
exterior of a circle All points of the plane that are outside a circle.
exterior of an angle All points not on the angle or in its interior. See also interior
of an angle.
external segment The part of a secant segment that is not inside the circle.
extremes of a proportion The first and last terms of a proportion. The
extremes of a/b = c/d are a and d.
flow proof 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 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.
geometric mean For two positive numbers a and b, the positive number x such
that a/x = x/b, or x= a•b.
geometric probability A probability that involves a geometric measure such as
length or area.
glide reflection A transformation in which every point P is mapped onto a point
P” 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 P.
great circle The intersection of a sphere and a plane that contains the center of
the sphere.
hemisphere Half of a sphere, formed when a great circle separates a sphere
into two congruent halves.
hypotenuse In a right triangle, the side opposite the right angle. See also legs
of a right triangle.
hypothesis The “if” part of a conditional statement.
icosahedron A polyhedron with twenty faces.
if-then form 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 The new figure that results from the transformation of a figure in a plane.
See also preimage.
incenter of a triangle The point of concurrency of the angle bisectors of a
triangle.
indirect proof 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 A process that includes looking for patterns and making
conjectures.
initial point of a vector The starting point of a vector. See also vector.
inscribed angle An angle whose vertex is on a circle and whose sides contain
chords of the circle.
inscribed polygon A polygon whose vertices all lie on a circle.
intercepted arc The arc that lies in the interior of an inscribed angle and has
endpoints on the angle. See also inscribed angle.
interior angles of a triangle When the sides of a triangle are extended, the
three original angles of the triangle.
interior of a circle All points of the plane that are inside a circle.
interior of an angle All points between the points that lie on each side of the
angle.
intersect To have one or more points in common.
intersection The set of points that two or more geometric figures have in
common.
inverse The statement formed when you negate the hypothesis and conclusion
of a conditional statement.
isometry A transformation that preserves lengths. Also called rigid
transformation.
isosceles trapezoid A trapezoid with congruent legs.
isosceles triangle A triangle with at least two congruent sides.
kite A quadrilateral that has two pairs of consecutive congruent sides, but in
which opposite sides are not congruent.
lateral area of a cylinder The area of the curved surface of a cylinder.
lateral area of a polyhedron The sum of the areas of the lateral faces of a
polyhedron.
Law of Detachment If p q is a true conditional statement and p is true, then q
is true.
Law of Syllogism If p q and q r are true conditional statements,
then p r is true.
legs of a right triangle In a right triangle, the sides that form the right angle.
legs of an isosceles triangle The two congruent sides of an isosceles triangle
that has only two congruent sides. See also base of an isosceles triangle.
length of a segment The distance between the endpoints of a segment. See
also distance between two points on a line.
line 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. See also undefined term.
line of symmetry A line that a figure in the plane has if the figure can be
mapped onto itself by a reflection in the line.
line perpendicular to a plane A line that intersects the plane in a point and is
perpendicular to every line in the plane that passes through that point.
line segment 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.
linear pair Two adjacent angles whose noncommon sides are opposite rays.
locus The set of all points that satisfy a given condition or a set of given
conditions. Plural is loci.
logical argument An argument based on deductive reasoning, which uses
facts, definitions, and accepted properties in a logical order.
magnitude of a vector The distance from the initial point to the terminal point of
a vector. The magnitude of AB is the distance from A to B and is written AB.
major arc Part of a circle that measures between 180° and 360°. See also minor
arc.
means of a proportion The middle terms of a proportion.
The means of a/b = c/d are b and c.
measure of a major arc The difference between 360° and the measure of its
associated minor arc.
measure of a minor arc The measure of its central angle.
measure of an angle Consider a point A on one side 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 TMOB is equal to the absolute value of the difference between the
real numbers for OA and OB .
median of a triangle A segment whose endpoints are a vertex of the triangle
and the midpoint of the opposite side.
midpoint The point that divides, or bisects, a segment into two congruent
segments.
midpoint formula If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then
the midpoint of AB has coordinates ((x1+ x2)/2, (y1+ y2)/2) .
midsegment of a trapezoid A segment that connects the midpoints of the legs
of a trapezoid.
midsegment of a triangle A segment that connects the midpoints of two sides
of a triangle.
minor arc Part of a circle that measures less than 180°. See also major arc.
negation The negative of a statement. The negation symbol is ~.
net A two-dimensional representation of all the faces of a polyhedron.
oblique prism 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.
obtuse angle An angle with measure between 90° and 180°.
obtuse triangle A triangle with one obtuse angle.
octahedron A polyhedron with eight faces.
opposite rays If C is between A and B, then CA and CB are opposite rays.
orthocenter of a triangle The point of concurrency of the lines containing the
altitudes of a triangle.
paragraph proof A type of proof written in paragraph form.
parallel lines Two lines that are coplanar and do not intersect. The symbol for
“is parallel to” is ||.
parallel planes Two planes that do not intersect.
parallel vectors Two vectors that have the same or opposite directions.
parallelogram A quadrilateral with both pairs of opposite sides parallel. The
parallelogram symbol is .
perpendicular bisector of a triangle A line, ray, or segment that is
perpendicular to a side of a triangle at the midpoint of the side.
perpendicular bisector A segment, ray, line, or plane that is perpendicular to a
segment at its midpoint.
perpendicular lines Two lines that intersect to form a right angle. The symbol
for “is perpendicular to” is .
plane 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.
Platonic solids 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 A point has no dimension. It is usually represented by a small dot. See
also undefined term.
point of concurrency The point of intersection of concurrent lines.
polygon 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 A solid that is bounded by polygons, called faces, that enclose a
single region of space. Plural is polyhedra, or polyhedrons.
postulates Rules that are accepted without proof. Also called axioms.
preimage The original figure in the transformation of a figure in a plane. See
also image.
prism 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.
proportion An equation that equates two ratios. Example: a/b = c/d
pyramid 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.
Pythagorean triple A set of three positive integers a, b, and c that satisfy the
equation c2 = a2 + b2.
radius of a circle 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.
radius of a polygon The radius of its circumscribed circle.
radius of a sphere 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.
ray Part of a line that consists of a point, called an initial point, and all points on
the line that extend in one direction.
rectangle A parallelogram with four right angles.
reduction A dilation with 0 < k < 1.
reflection 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.
regular polygon A polygon that is equilateral and equiangular.
regular polyhedron A polyhedron whose faces are all congruent regular
polygons.
regular pyramid 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.
rhombus A parallelogram with four congruent sides.
right angle An angle with measure equal to 90°.
right cone 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 A cylinder such that the segment joining the centers of the bases
is perpendicular to the bases.
right prism A prism whose lateral edges are perpendicular to both bases. See
also prism.
right triangle A triangle with one right angle.
rotation A type of transformation in which a figure is turned about a fixed point,
called the center of rotation.
rotational symmetry A figure in the plane has rotational symmetry if the figure
can be mapped onto itself by a rotation of 180° or less.
scale factor The ratio of the lengths of two corresponding sides of two similar
polygons.
scalene triangle A triangle with no congruent sides.
secant line A line that intersects a circle in two points.
secant segment A segment that intersects a circle in two points, with one point
as an endpoint of the segment.
sector of a circle The region bounded by two radii of a circle and their
intercepted arc.
segment bisector A segment, ray, line, or plane that intersects a segment at its
midpoint.
semicircle An arc whose endpoints are the endpoints of a diameter of the circle.
side opposite a vertex of a triangle A side of a triangle that does not contain
the given vertex.
similar polygons Two polygons such that their corresponding angles are
congruent and the lengths of corresponding sides are proportional. The symbol
for “is similar to” is .
similar solids Two solids with equal ratios of corresponding linear measures,
such as heights or radii.
sine A trigonometric ratio, abbreviated as sin. For right triangle ABC, the sine of
the acute angle A is sin A = side opposite A/hypotenuse
skew lines Two lines that do not intersect and are not coplanar.
solve a right triangle Determine the measurements of all sides and angles of a
right triangle.
special right triangles Right triangles whose angle measures are 45°- 45°- 90°
or 30°- 60°- 90°.
sphere The locus of points in space that are a given distance from a point,
called the center of the sphere.
square A parallelogram with four congruent sides and four right angles.
standard equation of a circle A circle with radius rand center (h, k) has this
standard equation: (x – h)2+ (y – k)2 = r2.
straight angle An angle with measure equal to 180°.
straightedge A construction tool used to draw segments. A ruler without marks.
sum of two vectors The sum of u = a1, b1 and v = a2, b2 is
u + v = a1+ a2, b1+ b2.
supplement The sum of the measures of an angle and its supplement is 180°.
supplementary angles Two angles whose measures have the sum 180°.
surface area of a cylinder The sum of the lateral area of the cylinder and the
areas of the two bases.
surface area of a polyhedron The sum of the areas of its faces.
tangent A trigonometric ratio, abbreviated as tan. For right triangle ABC, the
tangent of the acute angle A is tan A = side opposite A/ side adjacent to A.
tangent circles Circles that intersect in one point.
tangent line A line that intersects a circle in exactly one point, called the point of
tangency.
tangent segment A segment that is tangent to a circle at an endpoint.
terminal point of a vector The ending point of a vector. See also vector.
tetrahedron A polyhedron with four faces.
theorem A true statement that follows as a result of other true statements.
transformation The operation that maps, or moves, a preimage onto an image.
Three basic transformations are reflections, rotations, and translations.
translation 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. (2) PP QQ or PP and QQ are collinear.
transversal A line that intersects two or more coplanar lines at different points.
trapezoid A quadrilateral with exactly one pair of parallel sides, called bases.
The nonparallel sides are legs.
triangle A figure formed by three segments joining three noncollinear points,
called vertices. The triangle symbol is .
trigonometric ratio A ratio of the lengths of two sides of a right triangle. See
also sine, cosine, and tangent.
two-column proof A type of proof written as numbered statements and reasons
that show the logical order of an argument.
undefined term A word, such as point, line, or plane, that is not formally
defined, although there is general agreement about what the word means.
vector A quantity that has both direction and magnitude, and is represented by
an arrow drawn between two points.
vertex angle of an isosceles triangle The angle opposite the base of an
isosceles triangle. See also base of an isosceles triangle.
vertex of a polygon Each endpoint of a side of a polygon. Plural is vertices.
vertex of a polyhedron A point where three or more edges of a polyhedron
meet. See also polyhedron.
vertex of a triangle Each of the three points joining the sides of a triangle.
Plural is vertices. See also triangle.
vertical angles Two angles whose sides form two pairs of opposite rays.
volume of a solid The number of cubic units contained in the interior of a solid.