Download Glossary*Honors Geometry

Glossary— Geometry
Section
1.1
Term / Definition
Chapter One
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**Undefined Terms – Terms whose general meaning is assumed
and whose characteristics are understood only from the postulates or
axioms that use them.
1.1
**Point (undefined term) – A location with no size or
dimension. It is the most basic building block of geometry. In a two
dimensional coordinate system, a point’s location is represented by
an ordered pair of numbers (x, y).
1.1
**Line (undefined term) – A straight, continuous arrangement
of infinitely many points extending forever in two directions. A line
has length, but no width or thickness, so it is one-dimensional.
1.1
**Plane (undefined term) – A flat surface that extends infinitely
along its edges. A plane has length and width but no thickness, so it
is two-dimensional.
1.1
Definition – A statement that clarifies or explains the meaning of a
word or phrase.
1.1
Collinear – On the same line.
1.1
Coplanar – In the same plane.
1.1
Line Segment – Two points and all the points between them that
are collinear with the two points. Also called a segment. The
measure of a line segment is its length.
1.1
Endpoint – The point at either end of a segment or an arc, or the
first point of a ray
1.1
Congruent Segments – Line segments that are identical in shape
and size.
1.1
Bisect (segment) – To divide a segment into two congruent
segments.
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Section
Term / Definition
1.1
Midpoint – The point on the line segment that is the same distance
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from both endpoints. The midpoint bisects the segment.
1.1
Ray – A point on a line, and all the points of the line that lie on one
side of this point.
1.2
Angle (vertex and sides) – Two noncollinear rays (sides) having
a common endpoint (vertex).
1.2
Measure of an Angle –The smallest amount of rotation about the
vertex from one ray to the other, measured in degrees.
1.2
Degree – A unit of measure for angles and arcs equivalent to 1/360
of a rotation around a circle.
1.2
Reflex Measure – The largest amount of rotation less that 360°
about the vertex from one ray to the other, measured in degrees.
1.2
Protractor – A tool used to measure the size of an angle in degrees.
1.2
Congruent Angles – Angles that are identical in shape and size.
1.2
Angle Bisector – A ray that has its endpoint at the vertex of the
angle and that divides the angle into two congruent angles.
1.2
Incoming Angle – The angle formed between the path of an
approaching object and the surface from which it rebounds, such as a
billiard ball rolling toward a cushion or a ray of light traveling toward
a mirror.
1.2
Outgoing Angle – The angle formed between the path of a
rebounding object and the surface it collided with, such as a billiard
ball bouncing off a cushion or a ray of light reflecting off a mirror.
1.2
Adjacent Angles – Two non-overlapping angles with a common
vertex and one common side.
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Section
1.3
Term / Definition
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Counterexample – An example that shows a conjecture to be
incorrect or a definition to be inadequate.
1.3
Classify and Differentiate – Defining a term by categorizing it,
then distinguishing it from other members of the same group,
according to choose characteristics.
1.3
Perpendicular – Lines are perpendicular if they meet at 90 degree
angles. Line segments and rays are perpendicular if they lie on
perpendicular lines.
1.3
Parallel – Planes are parallel if they do not intersect. Figures are
parallel if they lie in parallel planes.
1.3
Skew Lines – Lines that are not in the same plane and do not
intersect.
1.3
Right Angle – An angle that measures 90 degrees.
1.3
Acute Angle – An angle that measures less than 90 degrees.
1.3
Obtuse Angle – An angle that measures between 90 degrees and
180 degrees.
1.3
Complimentary Angles – A pair of complementary angles has a
sum of 90 degrees.
1.3
Supplementary Angles – A pair of supplementary angles has a
sum of 180 degrees.
1.3
Vertical Angles – Angles formed by two intersecting lines, they
share a common vertex but not a common side.
1.3
Linear Pair – Two angles are a linear pair if they share a vertex
and a common side and their noncommon sides form a line.
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Section
Term / Definition
1.4
Polygon (vertex and sides) – A closed figure in a plane, formed
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by connecting line segments endpoint to endpoint with each segment
intersecting exactly two others.
1.4
Triangle – A polygon with 3 sides.
1.4
Quadrilateral – A polygon with 4 sides.
1.4
Pentagon – A polygon with 5 sides
1.4
Hexagon – A polygon with 6 sides.
1.4
Heptagon – A polygon with 7 sides.
1.4
Octagon – A polygon with 8 sides.
1.4
Nonagon – A polygon with 9 sides.
1.4
Decagon – A polygon with 10 sides.
1.4
Undecagon – A polygon with 11 sides.
1.4
Dodecagon – A polygon with 12 sides.
1.4
n-gon – A polygon with n sides.
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Section
1.4
Term / Definition
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Consecutive (angles, sides, or vertices of a polygon) –
Two angles that share a common side, two sides that share a common
vertex, or two vertices that are the endpoints of one side.
Consecutive sides are also called adjacent sides.
1.4
Diagonal – A line segment connecting two nonconsecutive vertices
of a polygon or polyhedron.
1.4
Convex Polygon – A polygon with no diagonal outside the
polygon.
1.4
Concave Polygon – A polygon with at least one diagonal outside
the polygon.
1.4
Congruent Polygons – Polygons that are identical in shape and
size.
1.4
Perimeter – The length of the boundary of a two-dimensional
figure. For a polygon, the perimeter is the sum of the lengths of its
sides.
1.4
Equilateral Polygon – Polygons in which all sides have equal
lengths.
1.4
Equiangular Polygon – Polygons in which all angles have equal
measures.
1.4
Regular Polygon – Polygons that are both equilateral and
equiangular.
1.5
Assume – To accept as true without facts or proof.
1.5
Right Triangle – A right triangle has one right angle.
1.5
Acute Triangle – An acute triangle has three acute angles.
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Section
Term / Definition
1.5
Obtuse Triangle – An obtuse triangle has one obtuse angle.
1.5
Scalene Triangle – A triangle with no congruent sides.
1.5
Equilateral Triangle – A triangle with three congruent sides.
1.5
Isosceles Triangle (vertex angle, base angles, and base) –
1.6
1.6
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A triangle with at least two congruent sides. The angle between the
two sides of equal length is called the vertex angle. The side
opposite the vertex angle is called the base. The two angles opposite
the two sides of equal length are called the base angles.
Trapezoid – A trapezoid is a quadrilateral with exactly one pair of
parallel sides.
Kite – A quadrilateral with two distinct pairs of consecutive
congruent sides.
1.6
Parallelogram – A quadrilateral with two pairs of parallel sides.
1.6
Rhombus - An equilateral parallelogram.
1.6
Rectangle – An equiangular parallelogram. (Each of the 4 angles
measures 90 degrees.)
1.6
Square – An equilateral rectangle. An equiangular rhombus. A
regular quadrilateral.
1.7
Circle (and its center) – The set of all points in a plane at a given
distance from a given point (called the center).
1.7
Radius – A line segment from the center of a circle or sphere to a
point on the circle or sphere. Also, the length of that line segment.
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Section
Term / Definition
1.7
Chord – A line segment whose endpoints lie on the circle.
1.7
Diameter – A chord that passes through the center. A diameter is
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the longest chord of a given circle.
1.7
Tangent Line (and its point of tangency) – A line that
intersects a circle only once. The point of intersection of a tangent
line and a circle is called the point of tangency.
1.7
Congruent Circles – Circles that are identical in shape and size.
1.7
Concentric Circles – Circles that share the same center.
1.7
Arc (of a circle) – Two points on a circle and the continuous part
of the circle between them.
1.7
Semicircle – An arc of a circle whose endpoints are the endpoints
of a diameter.
1.7
Minor Arc – An arc of a circle that is less than a semicircle.
1.7
Major Arc – An arc of a circle that is greater than a semicircle.
1.7
Arc Measure – The measure of the central angle that intercepts an
arc, measured in degrees.
1.7
Central Angle – An angle whose vertex is the center of a circle
and whose sides pass through the endpoints of an arc.
1.8
**Space (undefined term) – Thought of as the set of all points.
Space extends infinitely in all directions, so it is three-dimensional.
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Section
Term / Definition
1.8
Isometric Drawing – A drawing of a three-dimensional object that
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shows three faces in one view. Also called an edge view.
1.8
Solid with Examples of Solids – A three dimensional geometric
figure that completely encloses a region of space. Examples: cone,
cylinder, hemisphere, polyhedron, prism, pyramid, and sphere
1.8
Net – A two-dimensional pattern that can be folded to form a threedimensional figure.
1.8
Section – The intersection of a solid and a plane.
Chapter Two
2.1
Inductive Reasoning - The process of observing data,
recognizing patterns, and making generalizations about those
patterns.
2.1
Conjecture - A generalization resulting from inductive reasoning.
2.1
Rectangular Numbers - Numbers that can be represented by a
rectangular array of dots or squares.
2.2
Function Rule - A rule that, when applied to one set of
numbers, generates another set of numbers with at most one
output value for each input value.
2.2
Nth Term - The number that a function rule generates as
output for a counting number n.
2.2
Function Notation - A convention for expressing a function
rule in terms of its input. For example, f (x) is the output of
function f whose input is x.
2.2
Linear Function - A function rule that, when applied to
consecutive whole numbers, generates a sequence with a
constant difference between consecutive terms.
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Section
Term / Definition
2.2
Line of Best Fit - The line that passes closest to all of
a given collection of points.
2.4
Deductive Reasoning The process of showing that certain
statements follow logically from agreed upon assumptions and
proven facts.
2.5
Converse The statement formed by exchanging the “if” (the
antecedent) and the “then” (the consequent) of a conditional
statement.
2.5
Biconditional Statement – a statement that includes both a
conditional statement and its converse, usually written in “if
and only if” form
2.6
Transversal - A line that intersects two or more other
coplanar lines.
2.6
Corresponding Angles - Two angles formed by a transversal
intersecting two lines that lie in the same position relative to
the two lines and the transversal.
2.6
Alternate Interior Angles - A pair of angles, formed by a
transversal intersecting two lines, that lie between the two lines
and are on opposite sides of the transversal.
2.6
Alternate Exterior Angles - A pair of angles, formed by a
transversal intersecting two lines, that do not lie between the
two lines and are on opposite sides of the transversal.
2.6
Consecutive Interior Angles - A pair of angles, formed by a
transversal intersecting two lines, that lie between the two lines
and are next to one another.
2.6
Consecutive Exterior Angles - A pair of angles, formed by a
transversal intersecting two lines, that do not lie between the
two lines and are next to one another.
3.2
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Chapter Three
Segment Bisector - A line, ray, or segment that passes
through the midpoint of a line segment in a plane.
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Section
Term / Definition
3.2
Perpendicular Bisector - A line that divides a line segment
into two congruent parts and is perpendicular to the line
segment.
3.2
Coincide - To lie exactly on top of each other.
3.2
Equidistant - Equally distant.
3.2
Median - A line segment connecting a vertex of a triangle to
the midpoint of the opposite side.
3.2
Midsegment - A line segment connecting the midpoints of
two sides.
3.3
Distance - (from a point to a line or plane) The length of the
perpendicular line segment from the point to the line or plane.
3.3
Altitude (of a triangle) - A perpendicular segment from a
vertex to the base or to the line containing the base.
3.3
Height - The length of an altitude.
3.4
Angle Bisector - (of a triangle) A segment that lies on an
angle bisector and that has one endpoint at the vertex and the
other on the opposite side of the triangle.
3.7
Concurrent Lines Two or more lines that intersect in a single
point.
3.7
Point of Concurrency - The point at which two or more
lines, line segments, or rays intersect.
3.7
Incenter - The point of concurrency of a triangle’s three angle
bisectors.
Picture
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Section
Term / Definition
3.7
Circumcenter - The point of concurrency of a triangle’s three
perpendicular bisectors.
3.7
Orthocenter - The point of concurrency of a triangle’s three
altitudes (or of the lines containing the altitudes).
3.7
Circumscribed - (about a circle) Having all sides tangent to
the circle, such as a triangle circumscribed about a circle.
(about a polygon) Passing through each vertex of the polygon,
such as a circle circumscribed about a triangle.
Inscribed - (in a polygon) Intersecting each side of the
polygon exactly once, such as a circle inscribed in a triangle.
(in a circle) Having each vertex on the circle, such as a triangle
inscribed in a circle.
Centroid - The point of concurrency of a triangle’s three
medians.
3.7
3.8
3.8
Center of Gravity - The balancing point of an object.
4.1
Chapter Four
Paragraph Proofs - A logical explanation presented in the
form of a paragraph.
4.1
Auxiliary Line - An extra line or line segment drawn
in a figure to help in a proof.
4.2
Leg (of an isosceles triangle) - One of the congruent sides of
an isosceles triangle.
4.3
Exterior Angle - An angle that forms a linear pair with one of
the interior angles of a polygon.
4.3
Adjacent Interior Angle - The angle of a polygon that forms
a linear pair with a given exterior angle of a polygon.
Picture
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Section
Term / Definition
4.3
Remote Interior Angles - (of a triangle) The interior angles
of a triangle that do not share a vertex with a given exterior
angle.
4.4
Included Angle - An angle formed between two consecutive
sides of a polygon.
4.5
Included Side - A side of a polygon between two consecutive
angles.
4.7
Flowchart Proof - A logical argument presented in the form
of a flowchart.
5.3
Picture
Chapter Five
Kite (vertex angles and non-vertex angles) A quadrilateral
with exactly two distinct pairs of congruent consecutive sides.
Vertex angles - The angles between the pairs of congruent
sides. Nonvertex angles - The two angles between
consecutive noncongruent sides of a kite.
5.3
Trapezoid (bases and base angles) - A quadrilateral with
exactly one pair of parallel sides. Bases - The two parallel
sides. Base angles - A pair of angles with a base of the
trapezoid as a common side.
5.3
Isosceles Trapezoid- A trapezoid whose two nonparallel
sides are congruent.
5.4
Midsegment (of a trapezoid)- The line segment connecting
the midpoints of the two nonparallel sides
5.5
Vector- A quantity that has both magnitude and direction. A
vector is represented by an arrow whose length and direction
represent the magnitude and direction of the vector.
5.5
Resultant Vector- The result of adding two vectors. Also
called a vector sum.
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Section
5.7
Term / Definition
Picture
Dart - A concave kite.
Chapter Ten (Probability)
10.1
Random Processes -
10.1
Fair -
10.1
Random Numbers -
10.1
Simulation -
10.1
Outcomes -
10.1
Event -
10.1
Simple Event -
10.1
Compound -
10.1
Experimental Probabilities -
10.1
Theoretical Probability -
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Section
Term / Definition
10.1
Geometric Probability
10.2
Tree Diagram
10.2
Independent
10.2
Dependent Events
10.2
Conditional Probability
10.3
Mutually Exclusive
10.3
Intersection
10.3
Union
10.3
Complements
10.4
Expected Value
10.4
Random Value
10.4
Discrete Random Variables
Picture
14
Section
Term / Definition
10.4
Geometric Random Variables
10.5
Counting Principle
10.5
Permutation
10.5
Factorial
10.6
Combination
10.7
Pascal’s Triangle
10.7
Expansion
10.7
Sample
10.7
Population
7.1
Chapter Seven
Image - The result of moving all points of a figure according
to a transformation.
7.1
Picture
Transformation - A rule that assigns to each point of a figure
another point in the plane, called its image.
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Section
Term / Definition
7.1
Rigid Transformation or Isometry - A transformation that
preserves size and shape. The image of a figure under an
isometry is congruent to the original figure. Also called a rigid
transformation.
7.1
Nonrigid Transformation - A transformation that does not
preserve the size of the original figure, such as an enlargement
or reduction.
7.1
Translation - An isometry in which each point is moved by
the same translation vector.
7.1
Translation Vector - A directed line segment from a point to
its translated image.
7.1
Rotation - An isometry in which each point is moved by the
same angle measure in the same direction along a circular path
about a fixed point.
7.1
Angle of Rotation - The angle between a point and its image
under a rotation, with its vertex at the center of the rotation and
sides that go through the point and its image.
7.1
Reflection / Line of Reflection - An isometry in which every
point and its image are on opposite sides and the same distance
from a fixed line. Line of reflection - The line across which
every point of a figure is moved by a reflection.
7.1
Point Symmetry - The property that a figure coincides with
itself under a rotation of 180°. Also called two-fold rotational
symmetry.
7.4
Tessellation or Tiling - A repeating pattern of shapes that
completely cover a plane without overlaps or gaps.
7.4
Monohedral Tessellation - A tessellation that uses only one
shape.
7.4
Regular Tessellation - A tessellation of congruent regular
polygons.
Picture
16
Section
Term / Definition
7.4
Vertex Arrangement or Numerical Name - A notation that
uses positive integers and other symbols to describe the
arrangement of regular polygons about vertices of a
semiregular tessellation. Also called the numerical name.
Semiregular Tessellation - A tessellation of two or more
different kinds of regular polygons that meet in the same order
at each vertex.
7.4
7.4
Picture
Archimedean Tilings - A regular or semiregular tessellation.
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