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RELC2 CMP3 UNIT 3
SYMMETRY AND TRANSFORMATION
84
Mathematics
8th Grade
02/23/2014

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Term
Acute angle
Definition
An angle that measures less than 90º and greater than 0°
Term
Altitude
Definition

The perpendicular distance from a vertex in a polygon to its opposite side.

Term
Angle .
Definition

Two rays extending from a common end point called the vertex. Angles are measured in degrees

Term
Base (geometric)
Definition

The line or plane of a geometric figure, from which an altitude can be constructed, upon which a figure is thought to rest.

Term
Capacity
Definition

The amount of space that can be filled in a container. Both capacity and volume are used to measure three-dimensional spaces; however, capacity usually refers to fluids, whereas volume usually refers to solids.

Term
Central angle
Definition

An angle that has its vertex at the center of a circle, with radii as its sides.

Term
Circle graph
Definition

A data display that divides a circle into regions representing a portion of the total set of data. The circle represents the whole set of data.

Term
Circumference
Definition
The perimeter of a circle.
Term
Closed figure
Definition

A two-dimensional figure that divides the plane in which the figure lies into two parts—the part inside the figure and the part outside the figure (e.g., circles, squares, rectangles).

Term
Complementary angles
Definition
Two angles with measures that sum to be exactly 90°
Term
Congruent
Definition

Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations).

Term
Customary units
Definition

The units of measure developed and used in the United States.
Customary units for:

• length are inches, feet, yards, and miles.
• weight are ounces, pounds, and tons.
• volume are cubic inches, cubic feet, and cubic yards.
• capacity are fluid ounces, cups, pints, quarts, and gallons.

Term
Cylinder
Definition

A three-dimensional figure with two parallel bases that are congruent circles.

Term
Dilation
Definition

A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.

Term
Diameter
Definition

A line segment from any point on the circle passing through the center to another point on the circle.

Term
Direct measure
Definition

Obtaining the measure of an object by using measuring devices, either standard devices of the customary or metric systems, or nonstandard devices such as a paper clip or pencil.

Term
Equilateral triangle
Definition
A triangle with three congruent sides.
Term
Face
Definition

One of the plane surfaces bounding a three-dimensional figure; a side.

Term
Height
Definition

A line segment extending from the vertex or apex of a figure to its base and forming a right angle with the base or the plane that contains the base.

Term
Hypotenuse
Definition

The longest side of a right triangle; the side opposite the right angle.

Term
Indirect measure
Definition

The measurement of an object through the known measure of another object.

Term
Intersection
Definition
The point at which two lines meet.
Term
Isosceles triangle
Definition
A triangle with two congruent sides and two congruent angles.
Term
Length
Definition

A one-dimensional measure that is the measurable property of line segments.

Term
Line
Definition

A collection of an infinite number of points in a straight pathway with unlimited length and having no width

Term
Line segment
Definition

A portion of a line that consists of a defined beginning and endpoint and all the points in between.

Term
Mass
Definition
The amount of matter in an object.
Term
Metric units
Definition

The units of measure developed in Europe and used in most of the world. Like the decimal system, the metric system uses the base 10. Metric units for:
• length are millimeters, centimeters, meters, and kilometers.
• mass are milligrams, grams, and kilograms.
• volume are cubic millimeters, cubic centimeters, and cubic
meters.
• capacity are milliliters, centiliters, liters, and kiloliters.

Term
Midpoint of a line
segment
Definition

The point on a line segment that divides it into two equal parts.
Term
Nonstandard units of
measure
Definition

Objects such as blocks, paper clips, crayons, or pencils that can be used to obtain a measure.

Term
Obtuse angle
Definition
An angle with a measure of more than 90º but less than 180º.
Term
Origin
Definition

The point of intersection of the x- and y-axes in a rectangular coordinate system, where the x-coordinate and y-coordinate are both zero (0).

Term
Parallel lines
Definition

Two lines in the same plane that are a constant distance apart. Parallel lines never meet and have equal slopes.

Term
Perimeter
Definition
The distance around a polygon.
Term
Perpendicular
Definition

Two lines, two line segments, or two planes that cross to form a right angle.

Term
Pi (π)
Definition

The symbol designating the ratio of the circumference of a circle to its diameter. It is an irrational number with common approximations of either 3.14 or 22/7.

Term
Planar cross-section
Definition
The intersection of a plane and a three-dimensional figure.
Term
Plane
Definition

An undefined, two-dimensional geometric surface that has no depth and no boundaries specified. A plane is determined by defining at least three distinct points or at least two distinct lines existing on the plane.

Term
Plane figure
Definition
A two-dimensional figure that lies entirely within a single plane.
Term
Point
Definition

A specific location in space that has no discernible length or width.

Term
Polygon
Definition

A closed-plane figure, having at least three sides that are line segments and are connected at their end-points.

Term
Pyramid
Definition

A three-dimensional figure whose base is a polygon and whose faces are triangles with a common vertex.

Term
Pythagorean theorem
Definition

The square of the hypotenuse (c) of a right triangle is equal to the sum of the square of the legs (a and b), as shown in the equation c2 = a2 + b2.

Term
Quadrant
Definition

Any of the four regions formed by the axes in a rectangular coordinate system.

Term
Radius
Definition

A line segment extending from the center of a circle or sphere to a point on the circle or sphere. Plural: radii.

Term
Ray
Definition

A portion of a line that begins at an endpoint and goes on indefinitely in one direction.

Term
Reflection
Definition

A transformation that produces the mirror image of a geometric figure over a line of reflection.

Term
Regular polygon
Definition

A polygon that is both equilateral (all sides congruent) and equiangular (all angles congruent).

Term
Right angle
Definition
An angle whose measure is exactly 90º.
Term
Right circular cylinder .
Definition

A cylinder in which the bases are parallel circles, perpendicular to the side of the cylinder

Term
Right prism or
rectangular solid
Definition

A three-dimensional figure (polyhedron) with congruent, polygonal bases and lateral faces that are all parallelograms.

Term
Rigid motion
Definition

A transformation of points in space consisting of a sequence of one or more translations, reflections, and/or rotations. Rigid motions here are assumed to preserve distances and angle measures.

Term
Rotation
Definition

A transformation of a figure by turning it counterclockwise about a center point or axis. The amount of rotation is usually expressed in the number of degrees (e.g., a 90º rotation).

Term
Scalene triangle
Definition
A triangle having no congruent sides.
Term
Scale factor
Definition

The constant that is multiplied by the length of each side of a figure that produces an image that is the same shape as the original figure, but a different size.

Term
Scale model
Definition

A model or drawing based on a ratio of the dimensions for the model and the actual object it represents.

Term
Scale
Definition

The numeric values, set at fixed intervals, assigned to the axes of a graph.

Term
Side
Definition

The edge of a polygon (e.g., a triangle has three sides) or one of the rays that make up an angle.

Term
Similar figures
Definition

Figures that are the same shape, have corresponding, congruent
angles, and have corresponding sides that are proportional in length.

Term
Similarity
Definition

A term describing figures that are the same shape but are not
necessarily the same size or in the same position.

Term
Solid figures
Definition

Three-dimensional figures that completely enclose a portion of space (e.g., a rectangular solid, cube, sphere, right circular cylinder, right circular cone, and square pyramid).

Term
Sphere
Definition

A three-dimensional figure in which all points on the figure are
equidistant from a center point.

Term
Standard units of measure

Definition

Accepted measuring devices and units of the customary or metric system.

Term
Straight angle .
Definition
An angle that measures exactly 180º
Term
Supplementary angles
Definition
Two angles, the sum of which is exactly 180°
Term
Surface area of a
geometric solid

Definition

The sum of the areas of the faces and any curved surfaces of the figure that create the geometric solid.

Term
Symmetry
Definition

A term describing the result of a line drawn through the center of a figure such that the two halves of the figure are reflections of each other across the line

Term
Transformation
Definition

An operation on a geometric figure by which another image is created. Common transformations include reflections (flips), translations (slides), rotations (turns) and dilations.

Term
Transitive property
Definition

When the first element has a particular relationship to a second
element that in turn has the same relationship to a third element, the first has this same relationship to the third element (e.g., if a = b and b = c, then a = c).

Term
Transitivity principle for
indirect measurement

Definition

If the length of object A is greater than the length of object B, and the length of object B is greater than the length of object C, then the length of object A is greater than the length of object C. This principle applies to measurement of other quantities as well.

Term
Translation
Definition
A transformation in which every point in a figure is moved in the same direction and by the same distance.
Term
Transversal
Definition
A line that intersects two or more lines at different points.
Term
Vector
Definition

A quantity with magnitude and direction in the plane or in space defined by an ordered pair or triple of real numbers.

Term
Vertex
Definition

The common endpoint from which two rays begin (i.e., the vertex of an angle) or the point where two lines intersect; the point on a triangle or pyramid opposite to and farthest from the base.

Term
Vertical angles
Definition

The opposite or non-adjacent angles formed when two lines intersect

Term
Volume
Definition

The amount of space occupied in three dimensions and expressed in cubic units. Both capacity and volume are used to measure empty spaces; however, capacity usually refers to fluids, whereas volume usually refers to solids.

Term
Weight
Definition
Measures that represent the force of gravity on an object.
Term
BASIC DESIGN ELEMENT
Definition

a part of a pattern or design that, when transformed using at least one type of symmetry transformation, will produce the entire design

Term
center of rotation
Definition
a fixed point about which a figure rotates
Term
line of symmetry
Definition
divides a figure into halves that are mirror images
Term
line of reflection
Definition

a transformation that maps each point of a figure to its mirror image. where a line acts as athe mirror.

Term
reflectional symmetry
Definition
line of symmetry divides a figure into halves
Term
rotational symmetry
Definition

a figure or design that if rotated less than a full turn about a point to a position in which it looks the same as the original

Term
similarity transformation
Definition

a transformation that produces similar figures. the image of a figure under transformation has the same shape as the original figure but may be a different size

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