Geometry, Measurement, and Density Vocabulary

A vocabulary flashcard set defining essential geometric terms, area and volume formulas, proportions, scale factor, formula rearrangements, and density definitions.

Complementary Angles

Two angles whose measures add up to $90^\circ$.

Supplementary Angles

Two angles whose measures add up to $180^\circ$.

Vertical Angles

Opposite angles formed when two lines intersect. Vertical angles are congruent (equal).

Linear Pair

Two adjacent angles that form a straight line. Their measures add to $180^\circ$.

Area of a Rectangle

$A = lw$ — Area = length $\times$ width.

Area of a Triangle

$A = \frac{1}{2}bh$ — multiply base $\times$ height and divide by $2$.

Area of a Parallelogram

$A = bh$ — base $\times$ perpendicular height.

Area of a Trapezoid

$A = \frac{1}{2}(b_1 + b_2)h$.

Radius

The distance from the center of a circle to its edge.

Diameter

The distance across a circle through its center ($d = 2r$).

Circumference

$C = 2\pi r$ or $C = \pi d$.

Area of a Circle

$A = \pi r^2$.

Pythagorean Theorem Applicability

Can only be used with a right triangle.

Pythagorean Theorem Variables ($a$, $b$, $c$)

$a$ and $b$ are the legs. $c$ is the hypotenuse, the longest side opposite the right angle.

Congruent

Figures have the same size and same shape.

Similar

Figures have the same shape, but may be different sizes. Corresponding angles are equal and corresponding sides are proportional.

Proportion

An equation stating that two ratios are equal, such as $\frac{2}{3} = \frac{8}{12}$.

Scale Factor

A number used to enlarge or reduce a figure while keeping the same shape, found by: New length $\div$ original length.

Units for Area

Square units, such as $\text{ft}^2$, $\text{in}^2$, or $\text{cm}^2$.

Units for Volume

Cubic units, such as $\text{ft}^3$, $\text{in}^3$, or $\text{cm}^3$.

General Volume Formula for a Prism

$V = Bh$, where $B$ is the area of the base and $h$ is the height.

Volume of a Rectangular Prism

$V = lwh$.

Volume of a Cylinder

$V = \pi r^2 h$.

Volume of a Pyramid

$V = \frac{1}{3}Bh$.

Volume of a Cone

$V = \frac{1}{3}\pi r^2 h$.

One-Third ($\frac{1}{3}$) Volume Relationship

A pyramid or cone with the same base and height as a corresponding prism or cylinder has one-third ($\frac{1}{3}$) its volume.

Rearranging Formulas

Isolating the requested variable by using inverse operations while keeping the equation balanced.

Density

Describes how much mass is packed into a given volume, calculated using $D = \frac{m}{V}$ (density = mass $\div$ volume).

Mass Formula (from Density)

$m = DV$.

Volume Formula (from Density)

$V = \frac{m}{D}$.