Two-Dimensional Figures, Transformations, and Three-Dimensional Solids

This set of vocabulary flashcards covers key geometry concepts including polygon classification, area and perimeter formulas, rigid transformations in the coordinate plane, and surface area and volume of three-dimensional solids.

Polygon Sides

The geometric figure that comprises the sides of a polygon is a line segment.

Regular Polygon

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

Perimeter ($P$)

The distance around a polygon, calculated as the sum of all its side lengths.

Circumference ($C$)

The distance around a circle, calculated using the formulas $C = 2\times \text{π} \times r$ or $C = \text{π} \times d$.

Area of a Trapezoid

The measurement of the surface of a trapezoid, found using the formula $A = \frac{1}{2}h(b_1 + b_2)$, where $h$ is height and $b_1, b_2$ are the bases.

Rigid Transformation

A transformation that creates congruent figures because it does not change the shape or size of the original figure.

Translation

A rigid transformation that slides a figure to a different location while maintaining its original orientation.

Reflection

A rigid transformation that flips a figure to create a mirror image (an inverted exact version).

Rotation

A rigid transformation that turns or spins a figure around a specific point.

Reflection in the x-axis

A coordinate transformation where the point $(a, b)$ becomes $(a, -b)$.

Reflection in the y-axis

A coordinate transformation where the point $(a, b)$ becomes $(-a, b)$.

Translation along a Vector

A coordinate transformation where the point $(a, b)$ translated along vector $\text{⟨}x, y\text{⟩}$ becomes $(a + x, b + y)$, as seen in the mapping $(x, y) \rightarrow (x + a, y + b)$.

180° Rotation about the Origin

A coordinate transformation where the preimage $(x, y)$ maps to the image $(-x, -y)$.

90° Counterclockwise Rotation

A coordinate transformation where the preimage $(x, y)$ maps to the image $(-y, x)$.

270° Counterclockwise Rotation

A coordinate transformation where the preimage $(x, y)$ maps to the image $(y, -x)$.

Polyhedron

A three-dimensional solid made up of flat surfaces; examples include prisms and pyramids.

Non-polyhedron

Three-dimensional solids that have curved surfaces; examples include spheres, cylinders, and cones.

Surface Area ($S$ or $SA$)

The measurement of the total surface of a solid figure, labeled in square units.

Volume ($V$)

The measurement of the amount of space that a solid encloses, labeled in cubic units (e.g., $\text{cm}^3$, $\text{in}^3$).

Slant Height ($l$)

The distance from the apex of a pyramid or cone down the side to the edge of the base; it is distinct from the vertical height ($h$).

Surface Area of a Sphere

Calculated using the formula $S = 4\times \text{π} \times r^2$.

Volume of a Sphere

Calculated using the formula $V = \frac{4}{3}\times \text{π} \times r^3$.

Hemisphere

A three-dimensional figure that is exactly half of a sphere.

Surface Area of a Hemisphere

Calculated using the formula $S = 3\times \text{π} \times r^2$ (derived from $\frac{1}{2}(4B) + B$, where $B$ is the area of the base).

Volume of a Hemisphere

Calculated using the formula $V = \frac{2}{3}\times \text{π} \times r^3$.