Geometry and measurements

Triangle

polygon with three vertices and three sides

Rotation

a geometric transformation consisting of a turn of a shape about a point, often the origin

Rigid Transformation

A geometric transformation after which the image and pre-image are congruent (length and angle measure are preserved).

Example.

Translations, Reflections, Rotations, Glide Reflections

Semicircle

half of a circle formed by cutting a circle along its diameter

Face

the sides of the shape

Surface Area

The area of the outside surface of a three-dimensional object

Example.

Sphere: SA=4(π)r2

Reflection

a geometric transformation over a line that that produces a mirror image of the original object or image

Octagon

a polygon with eight sides and eight vertices

Volume

measure of the total three-dimensional space contained inside an object

Parallel Lines

Lines that never intersect (coplanar).

They have slopes that are congruent.

Example.

y=2x+4y=2x−5y=2x−5

Edge

where these faces meet

Square

rectangle with four congruent sides (four sides of the same measure)

Sphere

set of points in 3-dimensional space that are all the same distance from a given point (the center)

Example.

Ball

Right Prism

a prism that has the two bases aligned with each other vertically, creating sides that are perpendicular to the bases (meet the bases at right angles), creating rectangular faces

Example.

Right Pentagonal Prism

Circle

The set of all points equidistant (the same distance) from a given point (the center). Circles have no sides nor interior angles.

Polygon

a multi-sided, closed figure made up of vertices (corners) and edges (sides)

Diameter of a Circle

the length of a segment that goes from one point on a circle through its center, and continues on to another point on the other side of the circle

Right Angle

An angle measuring exactly 90°, such as the corner of a piece of paper.

All right angles are congruent

Lateral Surface Area

Term definition.

The sum of the areas of all faces excluding the base(s) of a solid object

Example.

For a soup can, the area of the curved part (what is normally covered by the label)

Vertices

the corners of the shape

Rhombus

Parallelogram with all sides of congruent length.

Slant height

the distance from the apex (top) to an edge of the base

Radius of a Circle

the distance from the center of a circle to a point on the circle

Circumference

the perimeter of a circle

Trapezoid

Quadrilateral with one pair of parallel sides and one pair of non-parallel sides

Oblique Prism

a prism with bases that are not exactly above/below each other, creating faces that are parallelograms (without right angles)

Example.

Oblique Hexagonal Prism

Rectangle

Parallelogram with four right (90°) angles. Both pairs of opposite sides are parallel. Sides do NOT need to be congruent, but can be.

Asymmetric

A shape that can not be split into at least one pair of mirror images.

Tessellation

A pattern of shapes that fit perfectly together

Vertices

the corners of a shape

Pentagon

a polygon with five sides and five vertices

Quadrilateral

polygon with four vertices and four sides

Example.

Parallelogram

Perimeter

the distance around the outside of a figure

Pyramid

a shape in three dimensions that has a polygon for a base and triangular faces that meet at a point (the apex)

Example.

Triangular pyramid

Area

the amount of surface inside of a figure

Hexagon

a polygon with six sides and six vertices

Symmetric

A shape that can be split into at least one pair of mirror images.

Regular Polygon

A polygon with all sides congruent to each other and all angle measures congruent to each other

Prism

a three-dimensional figure with quadrilateral faces with two congruent bases (and no apex)

Example.

Rectangular prism

Net

a two-dimensional representation or pattern for a three-dimensional object

Total Surface Area

The sum of all of the areas of all faces of a solid object

Example.

For a soup can, the area of the curved part plus the areas of the top and base

Translation

a geometric transformation consisting of a movement to the right or left, up or down, or a combination of movements

Parallelogram

Quadrilateral with two pairs of opposite sides that are parallel to each other