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Geometry Vocabulary
Name______________________________ Class_______________
Definition/Description Symbol/Sketch
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 ANote: capital letter is used
2 line
3a line segment
3b measurement of a line segment
4 endpoint Either of two points that mark the ends of a line segment.
A part of a line between two endpoints.
written: �read: line segment ABNote: the letters indicate the points at the beginning and the end of the line segmentNote: the drawing of a line segment has visible points while the symbol does not
AB
The length of a line segment.
written: � ex.: �read: measurement of line segment AB
AB AB = 5cm
An infinite set of points forming a straight path extending indefinitely in two directions.
written: �read: line ABNote: the drawing of a line has visible points while the symbol does notNote: named using any 2 points on the line
AB! "##
5 ray
6 intersecting lines Two lines that cross.
7 parallel lines
8 perpendicular lines
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
A portion of a line that has one endpoint and extends forever in one direction.
written: �read: ray ABNotes on symbol: the arrow on top of the symbol always points right; it is always 2 letters; first letter is always the endpointNote: the drawing of a ray has a visible point while the symbol does not
AB! "!!
Lines, segments or rays that intersect to form right angles.
symbol: ex. read: is perpendicular toNote: the drawing of perpendicular lines has a different symbol to indicate perpendicular (lines forming small square at intersection)
⊥ AB! "##
⊥ CD! "##
Two straight lines on a two-dimensional surface that never intersect and are the same distance apart.
symbol: ex. read: is parallel toNote: the drawing of parallel lines has different symbols (arrow heads on lines) to indicate parallel
! AB! "##$CD! "##
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
15b measurement of an angle
A geometric figure made up of two rays or line segments that have the same endpoint.
written: �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.
!ABC(or∠ABC) or !B(or∠B)
The amount an angle is “open”.The most common units used for measuring angles are degrees and radians.(See Definition #23.) written: �read: the measure(or measurement) of angle ABCexample: �
m∠ABC(or m!ABC)
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
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.
Represents � of a full rotation of a
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 � radians.
1360
°
π180
28 Triangle Sum Theorem
The theorem that states: the measures of the angles in a triangle add to 180°.
29 congruent
30 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.
Figures, segments, or angles that are the same size and same shape.
Symbol: read: is congruent to
Note: In a diagram, the same number of tick marks indicate that sides (or angles) are congruent.
≅
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
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.
For right triangles:
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
leg2 + leg2 = hypotenuse2
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
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.
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.symbol is written: �symbol is read: is similar toNote: congruent figures are (a special type of) similar with a scale factor of 1.
∼
49 center (of a circle) The point equidistant from all points on a circle.
50 radius(plural: radii)
The distance from the center to a point on a circle.
51 chord A line segment that connects two points on a circle.
Note: the endpoints of the chord are on the circle.
52 diameter A chord (or line segment that has its endpoints on the circle) that passes through the center.
53 circumference
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.
The distance around the outside of a circle. C = πd or (d=diameter, r=radius)
C = 2πr
56 pi (π)
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: �read: arc AB (minor arc)Note: minor arcs are named using 2 pointsNote: major arcs (including semicircles) are named using 3 pointsNote: Arcs have the same measure as their central angle. (See definition #63)
AB!
The ratio of the circumference of a circle to the length of its diameter.
π =
Cd! 3.14 or 22
7
62 semicircle
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.
An arc that represents half of a circle.
written: �read: semicircle ABC Notes: 3 points are needed to name semicircles; A and C are the endpoints of this semicircleNote: major arcs are named like semicircles
ABC!
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
(b = base, h = height)
87 perimeter of a square
P= 4s
(s=side length)
88 area of a square
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
91 area of a trapezoid
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.
(s = side)
A = s2
(h = height)
or A= average of bases � height
A =12h(top + bottom bases)
⋅
(b = base, h = height)
A =12bh
95 edge The line segment where two faces of a solid figure meet.
96 pyramid
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.
Note: Prisms can be right or oblique.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.
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
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
example: cu. cm or cm3
112 surface area of a prism
113 surface area of a cylinder
or
(r=radius, d=diameter, h=height)
SA = 2πr2 + 2πrhSA = 2πr2 + πdh
or (B=base area, L= lateral area, P=perimeter, h=height)
SA = 2B + L SA = 2B + Ph
114 volume of a prism
115 volume of a cylinder
116 volume of a pyramid
117 volume of a cone
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
120 transversal A line that intersects a system of lines.
(r=radius, h=height)
V =13πr2h
(r=radius, h=height)
V = πr2h
(B=base area, h=height)
V =13Bh
(B=base area, h=height)
V = Bh
�SA = πrs +πr2
(r=radius, s=slant height)
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 non-transversal 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 3-dimensional space with a plane (or of a body in 2-dimensional space with a line)
Index18 acute angle
33 acute triangle
17 adjacent angles
124 alternate angles
89 altitude of a triangle
15a angle
42 angle bisector
61 arc
58 area
60 area of a circle
86 area of a rectangle and/or parallelogram
88 area of a square
91 area of a trapezoid
90 area of a triangle
83 base (2-D)
104 base (3-D)
41 bisect
49 center (of a circle)
129 center of dilation
63 central angle
51 chord
48 circle
53 circumference
39 compass
24 complementary angles
92 composite figure
101 cone
29 congruent
135 constructions
121 corresponding angles
45 corresponding parts
136 cross section
99 cube
111 cubic unit
100 cylinder
72 decagon
23 degree
81 diagonal
52 diameter
128 dilation
74 dodecagon
95 edge
4 endpoint
30 equilateral triangle
123 exterior angles
94 face
57 formula
82 height
103 hemisphere
73 hendecagon
69 heptagon
68 hexagon
36 hypotenuse
126 image
122 interior angles
6 intersecting lines
75b isosceles trapezoid
31 isosceles triangle
80 kite
106 lateral area (of a prism)
105 lateral face (of a prism)
107 lateral surface (of a cylinder)
37 leg
2 line
25 linear pair
132 line of reflection
134 line of symmetry (a.k.a. axis of symmetry)
3a line segment
15b measurement of an angle
3b measurement of a line segment
40 midpoint
109 net
10 non-linear
71 nonagon
98c oblique prism
20 obtuse angle
34 obtuse triangle
70 octagon
7 parallel lines
13 parallel planes
75 parallelogram
67 pentagon
84 perimeter
87 perimeter of a square
85 perimeter of rectangle
43 perpendicular bisector
8 perpendicular lines
14 perpendicular planes
56 pi (π)
11 plane
1 point
26 polygon
93 polyhedron
98a prism
44 proportion
22 protractor
96 pyramid
38 Pythagorean Theorem
66 quadrilateral
23 radian
50 radius
55 rate
54 ratio
5 ray
77 rectangle
131 reflection
65 regular polygon
79 rhombus
19 right angle
98b right prism
75c right trapezoid
35 right triangle
130 rotation
47 scale factor
32 scalene triangle
64 sector
62 semicircle
46 similar
12 skew lines
118 slant height (of a pyramid or cone)
136 slice
102 sphere
78 square
59 square unit
21 straight angle
24b supplementary angles
108 surface area
119 surface area of a cone
113 surface area of a cylinder
112 surface area of a prism
133 symmetry
97 tetrahedron
125 transformation
127 translation (a.k.a slide)
120 transversal
75a trapezoid
27 triangle
28 Triangle Sum Theorem
73 undecagon
9 vertex (plural: vertices)
16 vertical angles
110 volume
117 volume of a cone
115 volume of a cylinder
114 volume of a prism
116 volume of a pyramid
