Unit 1 Vocabulary (IM 6th Grade)

side

A line segment in a polygon is called a side (it is also called an edge). Sometimes the faces of a polyhedron are called its sides.

edge

A line segment in a polygon is called an edge (it is also called a side). A line segment where two faces meet in a polyhedron is also called an edge.

net

A net is a two-dimensional representation of a polyhedron. It can be cut out and folded to make a model of the polyhedron. Here is a net for a cube.

parallelogram

A parallelogram is a four-sided polygon with two pairs of parallel sides. Here are two examples of parallelograms.

polygon

A polygon is a two-dimensional figure composed of a sequence of straight line segments, connected end-to-end, with the last one connecting back to the first. We call the line segments the edges or sides of the polygon. We call a point where the edges connect a vertex. The edges of a polygon never cross each other. The plural of vertex is vertices. A polygon always encloses a two-dimensional region.

polyhedron / polyhedra (example)

A polyhedron always encloses a three-dimensional region. Here are some drawings of polyhedra.

polyhedron (polyhedra)

A polyhedron is a three-dimensional figure with faces that are polygonal regions (filled-in polygons). Each face meets one and only one other face along a complete edge. The points where edges meet are called vertices. The plural of polyhedron is polyhedra.

prism

A prism is a type of polyhedron with two parallel faces that are identical copies of each other (called bases) connected by rectangles.

naming a prism

A prism is named for the shape of its bases; for example, if its base is a pentagon, then it is called a "pentagonal prism."

pyramid

A pyramid is a type of polyhedron that has one special face called the base. All of the other faces are triangles that all meet at a single vertex.

naming a pyramid

A pyramid is named for the shape of its base; for example, if its base is a pentagon, then it is called a "pentagonal pyramid."

quadrilateral

A quadrilateral is a four-sided polygon. A rectangle is a quadrilateral. A pentagon is not a quadrilateral.

Region

A two-dimensional region includes the interior of a circle or the interior of a polygon. A three-dimensional region includes the interior of a sphere or the interior of a cube.

vertex (vertices)

A vertex is a point where two edges meet in a polygon or a polyhedron.

square of a number / squaring a number

An expression with an exponent of 2 is sometimes called a square. The reason s^2 is called the square of s is that a square whose edge has length s has area s^2. The expression 3^2 is read as "3 to the second power" or "3 squared." We also write and say "centimeters squared."

cube of a number / cubing a number

An expression with an exponent of 3 is sometimes called a cube. The reason s^3 is called the cube of s is that a cube whose edge has length s has volume s^3. The expression is read as "2 to the third power" or "2 cubed." We also write and say "centimeters cubed."

face

Any flat surface on a three-dimensional figure is a face. A cube has 6 faces.

base and height of a parallelogram

Any of the four sides of a parallelogram can be chosen as a base. The term base can also refer to the length of this side. Once we have chosen a base, then a perpendicular segment from a point on the base of a parallelogram to the opposite side will always have the same length. We call that value the height. There are infinitely many line segments that can represent the height.

base and height of a triangle

Any of the three sides of a triangle can be chosen as a base. The term base can also refer to the length of this side. Once we have chosen a base, the corresponding height is the length of a perpendicular segment from the base to the vertex opposite it. The opposite vertex is the vertex that is not an endpoint of the base.

compose/decompose

Compose means "put together" and decompose means "take apart." We use the word "compose" to describe putting several geometric figures together to make a new figure.

Area

The area of a two-dimensional region, measured in square units, is the number of unit squares that cover the region without gaps or overlaps.

Area (Example)

The side length of each square is 1 centimeter. The area of the shaded region A is 8 square centimeters. The area of shaded region B is 1/2 square centimeters.

surface area

The surface area (in square units) is the number of unit squares it takes to cover all the surfaces of a three-dimensional figure without gaps or overlaps. Each square face of this cube has area 9 square centimeters, so the surface area of the cube is 6⋅9=54 square centimeters.

compose/decompose (example)

This figure on the left is composed of a square and two half-circles. It is decomposed into those pieces on the right.

rearrange

When we decompose a figure into pieces and put them back together in a different way, we are rearranging the pieces. Here is an example of a triangle that has been decomposed and rearranged into two squares.

opposite vertex

When you choose a side to be the base in a triangle, the vertex that is not an endpoint of the base is the opposite vertex. Point A is the opposite vertex to the base BC.

prism (example)

Here are some drawings of some prisms.

pyramid (example)

Here are some drawings of some pyramids.

base and height of a triangle (example)

Here are three pairs of bases and heights for the same triangle. The dashed segments in the diagrams represent heights.

base and height of a parallelogram (example)

Here are two examples of base/height pairs on a parallelogram.

Region (example)

Here are two examples of two-dimensional regions. Area is a measure of two-dimensional regions.

polygon (example)

Here is a polygon with five vertices A, B, C, D, and E and five edges (or sides): AB, BC, CD, DE, and EA.