Download 1 - shurenribetgeometryclass

1.Angle
Two rays sharing a common endpoint. Angles are typically measured in degrees or
radians.
Angle
2.Acute Angle
An angle that has measure less than 90°.
3.Adjacent Angles
Two angles in a plane which share a common vertex and a common side but do not
overlap. Angles 1 and 2 below are adjacent angles.
Adjacent
Angles
4.Apothem
The line segment from the center of a regular polygon to the midpoint of a
side, or the length of this segment. Same as the inradius; that is, the
radius of a regular polygon's inscribed circle.
Note: Apothem is pronounced with the emphasis on the first syllable with
the a pronounced as in apple (A-puh-thum).
5.Base
In plane geometry or solid geometry, the bottom of a figure. If the top is
parallel to the bottom (as in a trapezoid or prism), both the top and bottom
are called bases.
6.Chord
A line segment on the interior of a circle. A chord has both endpoints on
the circle.
7.Centroid
For a triangle, this is the point at which the three medians intersect. In
general, the centroid is the center of mass of a figure of uniform (constant)
density.
8.Circle
The locus of all points that are a fixed distance from a given point.
9.Circumference
A complete circular arc. Circumference also means the distance around
the the outside of a circle.
10.Collinear
Lying on the same line.
11.Concave
Non-Convex
A shape or solid which has an indentation or "cave". Formally, a geometric
figure is concave if there is at least one line segment connecting interior
points which passes outside of the figure.
12.Cone
A three dimensional figure with a single base tapering to an apex. The
base can be any simple closed curve. Often the word cone refers to a right
circular cone.
13.Congruent
Exactly equal in size and shape. Congruent sides or segments have the
exact same length. Congruent angles have the exact same measure. For
any set of congruent geometric figures, corresponding sides, angles,
faces, etc. are congruent.
Note: Congruent segments, sides, and angles are often marked.
Congruent Segments
Congruent Angles
All four sides of this
rhombus are marked
to show they are
congruent to each
other.
The marked angles
of this isosceles
triangle are
congruent to each
other.
14. Contrapositive
Switching the hypothesis and conclusion of a conditional statement and
negating both. For example, the contrapositive of "If it is raining then the
grass is wet" is "If the grass is not wet then it is not raining."
15.Convex
A geometric figure with no indentations. Formally, a geometric figure is
convex if every line segment connecting interior points is entirely contained
within the figure's interior.
16.Coplanar
Lying in the same plane. For example, any set of three points in space are
coplanar.
17.Corresponding
Two features that are situated the same way in different objects.
18.Cube
Regular Hexahedron
A regular polyhedron for which all faces are squares.
Note: It is one of the five platonic solids.
Cube
a = length of an edge
Volume = a3
Rotate me if your
browser is Java-enabled.
Surface Area = 6a2
19.Cylinder
A three-dimensional geometric figure with parallel congruent bases. The
bases can be shaped like any closed plane figure (not necessarily a circle)
and must be oriented identically.
Note: The word cylinder often refers to a right circular cylinder.
20.Decagon
A polygon with ten sides.
Decagon
Regular Decagon
21.Degree
A unit of angle measure equal to
of a complete revolution. There are
360 degrees in a circle. Degrees are indicated by the ° symbol, so 35°
means 35 degrees.
22.Diameter of a Circle or Sphere
A line segment between two points on the circle or sphere which passes
through the center. The word diameter is also also refers to the length of
this line segment.
23.Distance Formula
is the distance between points (x1, y1) and (x2,
The formula
y2).
24.Dodecagon
A polygon with 12 sides.
Dodecagon
Regular Dodecagon
25.Dilation
A transformation in which a figure grows larger. Dilations may be with
respect to a point (dilation of a geometric figure) or with respect to the
axis of a graph (dilation of a graph).
Note: Some high school textbooks erroneously use the word dilation to
refer to all transformations in which the figure changes size, whether the
figure becomes larger or smaller. Unfortunately the English language has
no word that refers collectively to both stretching and shrinking.
Pronunciation: Dilation (die-LAY-shun) has only three syllables, not four
26.Dodecahedron
Regular Dodecahedron
A polyhedron with 12 faces. A regular dodecahedron has faces that are all
regular pentagons.
Note: It is one of the five platonic solids.
Regular Dodecahedron
a = length of an edge
Rotate me if your
Volume =
browser is Java-enabled.
Surface Area =
27.Edge of a Polyhedron
One of the line segments making up the framework of a polyhedron. The
edges are where the faces intersect each other.
28.Equidistant
Equally distant. For example, any two points on a circle are equidistant
from the center.
29.Equilateral Triangle
A triangle with three congruent sides. Note: The angles of an equilateral
triangle are each 60°.
Equilateral Triangle
s = length of a side
30.Euler's Formula (Polyhedra)
The equation below:
(number of faces) + (number of vertices) – (number of edges) = 2
This formula is true for all convex polyhedra as well as many types of
concave polyhedra.
Note: Euler is pronounced "Oiler".
31.Evaluate
To figure out or compute. For example, "evaluate
out that the expression simplifies to 17.
" means to figure
32.Exterior Angle of a Polygon
An angle between one side of a polygon and the extension of an adjacent
side.
Note: The sum of the exterior angles of any convex polygon is 360°. This
assumes that only one exterior angle is taken at each vertex.
33.Face of a Polyhedron
One of the flat surfaces making up a polyhedron. Note: The faces of a
polyhedron are all polygons.
34.Formula
An expression used to calculate a desired result, such as a formula to find
volume or a formula to count combinations. Formulas can also be
equations involving numbers and/or variables, such as Euler's formula.
35.Geometry
The study of geometric figures in two dimensions (plane geometry) and
three dimensions (solid geometry). It includes the study of points, lines,
triangles, quadrilaterals, other polygons, circles, spheres, prisms, pyramids,
cones, cylinders, and polyhedra. Geometry typically includes the study of
axioms, theorems, and two-column proofs.
Among the various types of geometry are analytic geometry, Euclidean
geometry, and non-Euclidean geometry
36.Height
The shortest distance between the base of a geometric figure and its top,
whether that top is an opposite vertex, an apex, or another base.
37.Height of a Cone
The distance from the apex of a cone to the base. Formally, the shortest
line segment between the apex of a cone and the (possibly extended)
base. Altitude also refers to the length of this segment.
38.Height of a Cylinder
The distance between the bases of a cylinder. Formally, the shortest line
segment between the (possibly extended) bases. Altitude also refers to the
length of this segment.
39.Height of a Prism
The distance between the two bases of a prism. Formally, the shortest line
segment between the (possibly extended) bases. Altitude also refers to the
length of this segment.
40.Hexagon
A polygon with six sides.
Hexagon
Regular Hexagon
41.Altitude of a Triangle
Height of a Triangle
The distance between a vertex of a triangle and the opposite side. Formally,
the shortest line segment between a vertex of a triangle and the (possibly
extended) opposite side. Altitude also refers to the length of this segment.
Note: The three altitudes of a triangle are concurrent, intersecting at the
orthocenter.
42.Heptagon
A polygon with seven sides. Some authors also use the name septagon
instead of heptagon.
Heptagon
Regular Heptagon
43.Hypotenuse
The side of a right triangle opposite the right angle. Note: The hypotenuse
is the longest side of a right triangle.
44.Interior Angle
An angle on the interior of a plane figure.
Examples: The angles labeled 1, 2, 3, 4, and 5 in the pentagon below are
all interior angles. Angles 3, 4, 5, and 6 in the second example below are
all interior angles as well (parallel lines cut by a transversal).
Note: The sum of the interior angles of an n-gon is given by the formula (n
– 2)·180°. For a triangle this sum is 180°, a quadrilateral 360°, a pentagon
540°, etc.
45.Isosceles Trapezoid
A trapezoid with base angles that are the same. Consequently, the legs will
be congruent to each other as well.
46.Isosceles Triangle
A triangle with two sides that are the same length. Formally, an isosceles
triangle is a triangle with at least two congruent sides.
47.Lateral Surface Area
Lateral Area
The surface area of the lateral surfaces of a solid. Lateral surface area
does not include the area of the base(s).
48.Lateral Surface
Lateral Face
The face or surface of a solid on its sides. That is, any face or surface that
is not a base.
49.Linear Pair of Angles
A pair of adjacent angles formed by intersecting lines. Angles 1 and 2
below are a linear pair. So are angles 2 and 4, angles 3 and 4, and angles
1 and 3. Linear pairs of angles are supplementary.
50.Locus
A word for a set of points that forms a geometric figure or graph. For
example, a circle can be defined as the locus of points that are all the
same distance from a given point.
51.Major Arc
The longer of the two arcs between two points on a circle.
52.Midpoint Formula
is the formula for the midpoint between points (x1, y1) and (x2,
y2). Note that this is simply the average of the x-coordinates and the
average of the y-coordinates.
53.Minor Arc
The shorter of the two arcs between two points on a circle.
54.Nonagon
A polygon with nine sides.
Nonagon
Regular Nonagon
55.Oblique Cylinder
A cylinder with bases that are not aligned one directly above the other.
56.Oblique Pyramid
A pyramid with an apex that is not aligned above the center of the base.
Solid view: oblique pyramid with
a square base
Frame view: oblique pyramid with
a square base
h = height of the pyramid
B = area of the base
57.Obtuse Angle
An angle that has measure more than 90° and less than 180°.
58.Octagon
A polygon with eight sides.
Octagon
Regular Octagon
59.Parallelogram
A quadrilateral with two pairs of parallel sides.
60.Pentagon
A polygon with five sides.
Pentagon
Regular Pentagon
61.Point
The geometric figure formed at the intersection of two distinct lines.
62.Polyhedron
A solid with no curved surfaces or edges. All faces are polygons and all
edges are line segments.
63.Prism
A solid with parallel congruent bases which are both polygons. The bases
must be oriented identically. The lateral faces of a prism are all
parallelograms or rectangles.
64.Pyramid
A polyhedron with a polygonal base and lateral faces that taper to an apex.
A pyramid with a triangular base is called a tetrahedron.
Solid view: right regular
pyramid with a regular
Frame view: right regular
pyramid with a regular
pentagon as base
pentagon as base
65.Quadrilateral
Quadrangle
A polygon with four sides.
66.Ray
A part of a line starting at a particular point and extending infinitely in one
direction.
67.Rectangle
A box shape on a plane. Formally, a rectangle is a quadrilateral with four
congruent angles (all 90°).
68.Regular Polygon
A polygon for which all sides are congruent and all angles are congruent.
Regular Polygon Formulas
n = number of sides
s = length of a side
r = apothem (radius of inscribed
circle)
R = radius of circumcircle
Regular
Pentagon
Regular Hexagon
Sum of interior angles = (n – 2)·180°
Interior angle =
Area = (½)nsr
Regular
Heptagon
Regular Octagon
Regular
69.Right Angle
A 90° angle.
70.Secant Line
A line which passes through at least two points of a curve. Note: If the two
points are close together, the secant line is nearly the same as a tangent
line.
71.Line Segment
Segment
All points between two given points (including the given points themselves).
Example:
line segment
72.Solid
Geometric Solid
Solid Geometric Figure
The collective term for all bounded three-dimensional geometric figures.
This includes polyhedra, pyramids, prisms, cylinders, cones, spheres,
ellipsoids, etc.
73.Supplementary Angles
Two angles that add up to 180°.
74.Tangent Line
A line that touches a curve at a point without crossing over. Formally, it is
a line which intersects a differentiable curve at a point where the slope of
the curve equals the slope of the line.
Note: A line tangent to a circle is perpendicular to the radius to the point of
tangency.
75.Vertex
A corner point of a geometric figure. For a polygon, vertices are where
adjacent sides meet. For an angle, the vertex is where the two rays making
up the angle meet.
Note: If the figure is a curve or surface, the vertices are the points of
maximum curvature.