Download Geometric terms 7

Geometry Vocabulary
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Definition/Description
1
point
• An exact location in space.
• In two dimensions, an ordered pair
specifies a point in a coordinate plane:
(x,y)
• written and read: point A
Note: capital letter is used
2
line
An infinite set of points forming a straight
path extending indefinitely in two
directions.
!##"
written: AB
read: line AB
Note: the drawing of a line has visible points
while the symbol does not
Note: named using any 2 points on the line
3a
line segment
A part of a line between two endpoints.
written: AB
read: line segment AB
Note: the letters indicate the points at the
beginning and the end of the line segment
Note: the drawing of a line segment has visible
points while the symbol does not
3b
4
measurement of a
line segment
The length of a line segment.
endpoint
Either of two points that mark the ends
of a line segment.
written: AB
ex.: AB = 5cm
read: measurement of line segment AB
Symbol/Sketch
5
ray
A portion of a line that has one endpoint
and extends forever in one direction.
!!!"
written: AB
read: ray AB
Notes on symbol: the arrow on top of the symbol
always points right; it is always 2 letters; first
letter is always the endpoint
Note: the drawing of a ray has a visible point
while the symbol does not
6
intersecting lines
Two lines that cross.
7
parallel lines
Two straight lines on a two-dimensional
surface that never intersect and are the
same distance apart.
symbol: !
read: is parallel to
!##" !##"
ex. AB $ CD
Note: the drawing of parallel lines has different
symbols (tick marks on lines) to indicate parallel
8
perpendicular lines Lines, segments or rays that intersect to
form right angles.
!##" !##"
symbol: ⊥
ex. AB ⊥ CD
read: is perpendicular to
Note: the drawing of perpendicular lines has a
different symbol to indicate perpendicular (lines
forming small square at intersection)
9
vertex
(plural: vertices)
The point at which two rays, line
segments or lines meet.
Note: no points drawn (exaggerated) at vertices
10
non-linear
(adjective)
Describes a set of points that do not lie
on a straight line when connected.
Compare to… linear: a set of points that
do lie on a straight line when connected
11
plane
A flat surface that extends indefinitely in
all directions. It has no thickness.
12
skew lines
Lines that lie in different planes that are
neither parallel nor intersecting.
13
parallel planes
Planes that do not intersect.
14
perpendicular
planes
Planes that intersect to form right angles.
15a
angle
A geometric figure made up of two rays
or line segments that have the same
endpoint.
written: !ABC(or∠ABC) or !B(or∠B)
read: angle ABC or angle B
Note: Usually three letters are used to name an angle.
One can be used if the angle can not be mistaken for
any other angle.
15b
measurement of an The amount an angle is “open”.
The most common units used for
angle
measuring angles are degrees and radians.
(See Definition #23.)
written: m∠ABC(or m!ABC)
read: the measure(or measurement) of
angle ABC
example: m∠ABC = 45°
16
vertical angles
A pair of opposite, congruent angles
formed by intersecting lines.
17
adjacent angles
Angles that share a common side and
vertex but no common interior points
18
acute angle
An angle with a measure greater than 0°
and less than 90°.
19
right angle
An angle whose measure is 90°.
20
obtuse angle
An angle greater than 90°.
21
straight angle
An angle whose measure is 180°.
22
protractor
A tool used to draw or measure angles.
23
degree
Represents 1 of a full rotation of a
360
circle, usually denoted by the symbol: ° .
Degrees are used for measuring (plane)
angles and arcs.
Note: A degree is not an International System of
Units (SI) unit, as the SI unit for angles is radian,
but it is mentioned in the SI brochure as an
accepted unit. Because a full rotation equals 2π
radians, one degree is equivalent to π radians.
180
24
complementary
angles
Two angles whose measures add to 90°.
24b
supplementary
angles
Two angles whose measures add to 180°.
25
linear pair
Two adjacent, supplementary angles.
Together their non-shared sides (or rays)
will form a straight angle.
26
polygon
A two-dimensional closed figure made of
straight line segments (sides or edges)
connected end to end (at vertices).
27
triangle
A polygon with three sides.
28
Triangle Sum
Theorem
The theorem that states: the measures of
the angles in a triangle add to 180°.
29
congruent
Figures, segments, or angles that are the
same size and same shape.
Symbol: ≅
read: is congruent to
30
Note: In a diagram, the same number of
tick marks indicate that sides (or angles)
are congruent.
equilateral triangle A triangle with all sides equal.
31
isosceles triangle
A triangle with two sides of equal length.
32
scalene triangle
A triangle with no two sides of equal
length.
33
acute triangle
A triangle in which all three angles are
acute (less than 90°).
34
obtuse triangle
A triangle with an obtuse angle.
35
right triangle
A triangle with one right angle in it.
36
hypotenuse
In a right triangle, the longest side of the
triangle, opposite the right angle.
37
leg
Either of two shorter sides of a right
triangle.
38
Pythagorean
Theorem
For right triangles:
leg 2 + leg 2 = hypotenuse 2
Uses:
•to find the length of any third side of a right
triangle when other two are known
•to see if a given triangle is a right triangle
39
compass
A tool used to create a circle.
40
midpoint
The middle point of a line segment.
41
bisect
Divide (a line, angle shape, etc.) into two
equal parts.
42
angle bisector
A ray that divides an angle into two
congruent parts.
43
perpendicular
bisector
A line, segment or ray that divides a
segment into two congruent segments
and is perpendicular to the segment.
44
proportion
An equation of two equivalent ratios.
45
corresponding parts Points, edges (sides), or angles in
congruent or similar figures that are
arranged in similar ways.
46
similar
Figures that have the same shape but not
necessarily the same size. The lengths of
the corresponding sides are proportional
to one another; the corresponding angles
are congruent.
Note: congruent figures are (a special type of)
similar with a scale factor of 1.
47
scale factor
A ratio between two sets of
measurements.
scale factor = side ratio
48
circle
The set of all points in two dimensions
that are the same distance r from a fixed
point P. The fixed point P is called the
center of the circle and the distance r is
called the radius.
49
center (of a circle)
The point equidistant from all points on
a circle.
50
radius
The distance from the center to a point
on a circle.
51
chord
A line segment that connects two points
on a circle.
52
diameter
A chord (or line segment that has its
endpoints on the circle) that passes
through the center.
53
circumference
The distance around the outside of a
circle.
C = πd or C = 2π r
(d=diameter, r=radius)
54
ratio
A comparison of two numbers or
quantities. They are measured in the
same or similar units.
55
rate
A ratio that compares two quantities
measured in different types of units.
56
pi (π)
The ratio of the circumference of a circle
to the length of its diameter.
π=
C
22
! 3.14 or
d
7
57
formula
An equation that shows a mathematical
relationship.
58
area
The measure in square units of the
interior region of a plane figure or the
surface of a three-dimensional figure.
59
square unit
A square whose sides measure 1 unit in
length. Area is measured in square units.
written: sq. units or units2
example: sq. cm or cm2
60
area of a circle
A = πr2
(r = radius)
61
arc
The portion of a circle between two
points on a circle. Arcs can be major
(longer than a semicircle) or minor.
!
written: AB
read: arc AB (minor arc)
Note: major arcs (including semicircles) are
named using 3 points)
Note: Arcs have the same measure as their central
angle. (See definition #63)
62
semicircle
An arc that represents half of a circle.
!
written: ABC
read: semicircle ABC
Notes: 3 points are needed to name semicircles ;A
and C are the endpoints of this semicircle
Note: major arcs re named like semicircles
63
central angle
An angle whose vertex is the center of a
circle.
64
sector
A part of the interior of a circle bounded
by two radii and the arc between their
endpoints.
Note: looks like a piece/slice of pie
65
regular polygon
A polygon in which all sides are
congruent and all angles are congruent.
66
quadrilateral
A polygon with four sides. (some special
quadrilaterals: squares, rectangles,
trapezoids, parallelograms, rhombuses or
rhombi)
67
pentagon
A polygon with five sides.
68
hexagon
A polygon with six sides.
69
heptagon
A seven sided polygon.
70
octagon
A polygon with eight sides.
71
nonagon
A polygon with nine sides.
72
decagon
A ten sided polygon.
73
undecagon or
hendecagon
An eleven sided polygon.
74
dodecagon
A twelve sided polygon.
75a
trapezoid
A quadrilateral with exactly one pair of
parallel sides. (definition under debate)
Some special trapezoids are isosceles
trapezoids and right trapezoids. See
below.
75b
isosceles trapezoid
A trapezoid whose non-parallel sides are
congruent.
75c
right trapezoid
A trapezoid with a right angle.
76
parallelogram
A quadrilateral with both pairs of
opposite sides parallel.
77
rectangle
A quadrilateral with four right angles.
(Its two pairs of opposite sides are
parallel and congruent.)
78
square
A quadrilateral with four congruent sides
and four right angles.
Note: squares must be rhombi (or rhombuses)
and rectangles.
79
rhombus
A quadrilateral with four congruent
sides.
80
kite
A quadrilateral with two pairs of
adjacent, congruent sides.
81
diagonal
A diagonal connects two vertices of a
polygon but is not a side.
82
height
The perpendicular distance between two
bases, or between a vertex and a base.
83
base
(of a 2-D figure)
For a triangle, the base may be any side,
although it is usually the bottom one. For
a trapezoid, the two parallel sides are the
bases.
84
perimeter
The distance around a figure on a flat
surface.
85
perimeter of
rectangle
P= 2l + 2w or P= 2b+2h
(l= length, w=width, b=base , h=height)
86
area of a rectangle
and/or
parallelogram
A = bh
perimeter of a
square
P= 4s
87
(b = base, h = height)
(s=side length)
88
area of a square
A = s2
(s = side)
89
altitude of a triangle Height. The perpendicular distance from
a vertex to the opposite side (or its
extension) of a triangle.
90
area of a triangle
1
bh
2
(b = base, h = height)
91
area of a trapezoid
1
h(top + bottom bases)
2
(h = height)
A=
A=
or A= average of bases ⋅ height
92
composite figure
A figure made up of simple geometric
shapes (rectangles, circles, etc.).
93
polyhedron
A three-dimensional figure with no holes
in which all faces are polygons.
94
face
A flat side of a polyhedron.
95
edge
The line segment where two faces of a
solid figure meet.
96
pyramid
A polyhedron with a polygonal base and
whose other faces are triangles with a
common vertex. A pyramid is named for
the shape of its base.
Note:
v+ f = e+2
97
tetrahedron
A polyhedron with four faces. Also
known as a triangular pyramid
98a
prism
A polyhedron with and two parallel,
congruent bases. The remaining faces are
parallelograms. No holes are permitted
in the solid. A prism is named for the
shape of its base.
98b
right prism
A prism in which the joining edges and
faces are perpendicular to the base faces.
This applies if the joining faces are
rectangular.
98c
oblique prism
A prism in which the joining edges and
faces are not perpendicular to the base
faces. The joining faces are not
rectangular.
99
cube
A rectangular prism with 6 congruent
faces, all squares.
Note: Prisms can be right or oblique.
100
cylinder
Commonly, a three dimensional object
with two circular, congruent and parallel
bases. (A soda can.)
Note: Cylinders can be oblique (slanted).
101
cone
A three-dimensional figure with one
circular base and one vertex.
Note: Cones can be oblique.
102
sphere
A round 3-D figure.
Looks like a ball.
103
hemisphere
Half of a sphere.
104
base
(of a 3-D figure)
For a cylinder or a prism, either one of
the two congruent parallel faces may be
the base.
For a pyramid or cone, the base is the
(flat) face that does not contain the
vertex (where all the sides come
together).
105
lateral face
(of a prism)
Parallelograms that connect the bases.
106
lateral area
(of a prism)
The sum of the areas of the lateral faces.
107
lateral surface
(of a cylinder)
The curved surface that connects the
bases.
108
surface area
The total area of all faces and bases of a
polyhedron, cylinder, cone or pyramid.
109
net
A two dimensional one-piece plan which
can be folded into a three dimensional
shape.
110
volume
The number of cubic units inside a three
dimensional object.
111
cubic unit
A cube whose edges measure 1 unit in
length. Volume is measured in cubic
units.
written: cu. units or units3
112
surface area of a
prism
113
surface area of a
cylinder
example: cu. cm or cm3
SA = 2B + L or SA = 2B + Ph
(B=base area, L= lateral area,
P=perimeter, h=height)
SA = 2π r 2 + 2π rh or
SA = 2π r 2 + π dh
(r=radius, d=diameter, h=height)
114
volume of a prism
V = Bh
(B=base area, h=height)
115
volume of a
cylinder
V = π r 2h
(r=radius, h=height)
116
volume of a
pyramid
1
Bh
3
(B=base area, h=height)
117
volume of a cone
1
V = π r 2h
3
(r=radius, h=height)
118
slant height (of a
pyramid or cone)
The distance from the base to its vertex,
measured along the lateral surface.
119
surface area of a
cone
SA = π rs + π r 2
(r=radius, s=slant height)
120
transversal
A line that intersects a system of lines.
V=
121
corresponding
angles
The angles that occupy the same relative
position at each intersection when two
lines are intersected by a transversal. If
the two lines are parallel, the
corresponding angles are congruent.
122
interior angles
1) The angles located in the interior of a
polygon.
2) The angles located between the nontransversal lines when the lines are cut
by a transversal.
123
exterior angles
1) The outer angles formed by the side of
polygon and the adjacent side extended
outward.
2) The angles not located between the
non-transversal lines when the lines are
cut by a transversal.
124
alternate angles
Angles on opposite sides of a
transversal. Can be alternate interior
angles (aka “Z angles”) or alternate
exterior angles.
125
transformation
A change in the size or position of a
figure.
126
image
A figure resulting from a transformation.
127
translation (a.k.a
slide)
A transformation resulting in the
movement(slide) of a figure along a
straight line.
128
dilation
A transformation in which a figure is
enlarged or reduced by a given scale
factor around a given center point, called
the center of dilation.
129
center of dilation
A fixed point in the plane about which
all points are expanded or contracted.
130
rotation
A transformation in which a figure is
rotated or turned around a point.
131
reflection
A transformation of a figure that flips (or
reflects) the figure across a line.
132
line of reflection
A line that a figure is flipped across to
create a mirror image of the original
figure.
133
symmetry
Here are two types (not the only two):
• bilateral symmetry: half object is
mirror image of other half
• radial symmetry: new image is an
identical rotation of original figure
Note: the opposite of symmetry is
asymmetry.
134
line of symmetry
(a.k.a. axis of
symmetry)
A line that runs down the center of a
shape such that if the shape were folded
in half on this line, the two halves would
match up perfectly. The two halves
would be mirror images of one another.
135
construction
Various geometric objects created using
only a compass and a straightedge.
136
cross section or
slice
the intersection of a body in 3dimensional space with a plane (or of a
body in 2-dimensional space with a line)
18
acute angle
24
Index
complementary angles
33
acute triangle
92
composite figure
73
hendecagon
17
adjacent angles
101
cone
69
heptagon
124
alternate angles
29
congruent
68
hexagon
89
altitude of a triangle
135
constructions
36
hypotenuse
15a
angle
121
corresponding angles
126
image
42
angle bisector
45
corresponding parts
122
interior angles
61
arc
136
cross section
6
intersecting lines
58
area
99
cube
75b
isosceles trapezoid
60
area of a circle
111
cubic unit
31
isosceles triangle
86
100
cylinder
80
kite
88
area of a rectangle
and/or parallelogram
area of a square
72
decagon
106
91
area of a trapezoid
23
degree
105
90
area of a triangle
81
diagonal
107
83
base (2-D)
52
diameter
37
lateral area (of a
prism)
lateral face (of a
prism)
lateral surface (of a
cylinder)
leg
104
base (3-D)
128
dilation
2
line
41
bisect
74
dodecagon
25
linear pair
49
center (of a circle)
95
edge
132
line of reflection
129
center of dilation
4
endpoint
134
63
central angle
30
equilateral triangle
51
chord
123
exterior angles
line of symmetry
(a.k.a. axis of
symmetry)
line segment
48
circle
94
face
53
circumference
57
formula
3b
39
compass
82
height
40
measurement of an
angle
measurement of a line
segment
midpoint
109
net
103
hemisphere
3a
15b
10
non-linear
38
Pythagorean Theorem
78
square
71
nonagon
66
quadrilateral
59
square unit
98c
oblique prism
23
radian
21
straight angle
20
obtuse angle
50
radius
24b
supplementary angles
34
obtuse triangle
55
rate
108
surface area
70
octagon
54
ratio
119
surface area of a cone
7
parallel lines
5
ray
113
13
parallel planes
77
rectangle
112
75
parallelogram
131
reflection
133
surface area of a
cylinder
surface area of a
prism
symmetry
67
pentagon
65
regular polygon
97
tetrahedron
84
perimeter
79
rhombus
125
transformation
87
perimeter of a square
19
right angle
127
85
perimeter of rectangle
98b
right prism
120
translation (a.k.a
slide)
transversal
43
perpendicular bisector
75c
right trapezoid
75a
trapezoid
8
perpendicular lines
35
right triangle
27
triangle
14
perpendicular planes
130
rotation
28
56
pi (π)
47
scale factor
Triangle Sum
Theorem
undecagon
11
plane
32
scalene triangle
1
point
64
sector
26
polygon
62
semicircle
93
polyhedron
46
similar
98a
prism
12
skew lines
44
proportion
118
22
protractor
136
slant height (of a
pyramid or cone)
slice
96
pyramid
102
sphere
73
9
16
vertex (plural:
vertices)
vertical angles
110
volume
117
volume of a cone
115
volume of a cylinder
114
volume of a prism
116
volume of a pyramid