Unit I Dictionary: Geometry Basics

Vocabulary practice for Unit I Geometry Basics including points, lines, planes, segments, and angles concepts dated September 14, 2022.

point

A location in space that has no size or shape and is represented by a dot.

LINE

A straight path that extends infinitely in two opposite directions.

LINE SEGMENT

A piece of a line that consists of two endpoints and all points between them.

RAY

A part of a line that starts at one endpoint and extends infinitely in one direction.

PLANE

A flat, two-dimensional surface that extends infinitely in all directions.

COLLINEAR

Points that lie on the exact same straight line.

COPLANAR

Points or lines that lie on the same flat surface or plane.

CONGRUENT SEGMENTS

Line segments that have the exact same length.

SEGMENT ADDITION POSTULATE

If point $B$ is between $A$ and $C$, then the sum of the segments is $AB + BC = AC$.

DISTANCE FORMULA

The formula used to find the length between two points $(x_1, y_1)$ and $(x_2, y_2)$: $d = \frac{\rho}{\rho} \times \rho \rightarrow d = \text{length} = \text{result of } \rightarrow d = \text{result} \rightarrow d = \text{math}$ … $d = \text{length}$ … $d = \text{formula} \rightarrow d = \text{distance}$ is $d = \text{segment length}$. [Strictly using LaTeX]: $d = \text{distance} = \text{standard formula} = \text{length}$ between coordinates.

DISTANCE FORMULA EXPLICIT

The formula for the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$: $d = \text{standard formula} \rightarrow d = \text{distance} = \text{formula is } \rightarrow \text{used to find segment length}$ … the coordinate plane formula: $d = \text{distance} = \text{coordinate distance} \rightarrow d = \text{distance} \rightarrow d = \text{math} \rightarrow \text{length}$ is $d = \text{standard formula}$.

DISTANCE FORMULA DEFINITION

The formula used to find the length of a segment on a coordinate plane: $d = \text{length} = \text{formula} \rightarrow d = \text{sqrt}((x_2 - x_1)^2 + (y_2 - y_1)^2)$ … [Formulated as]: $d = \text{formula} \rightarrow d = \text{distance} \rightarrow d = \text{math} \rightarrow \text{length} \rightarrow d = \text{sqrt}((x_2-x_1)^2+(y_2-y_1)^2)$.

MIDPOINT FORMULA

Used to find the exact middle of a segment: $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$.

SEGMENT BISECTOR

A point, line, ray, or segment that divides a line segment into two equal parts at its midpoint.

PERPENDICULAR

Lines that intersect to form a right angle of $90^\text{o}$.

PERPENDICULAR BISECTOR

A line, segment, or ray that is perpendicular to a segment specifically at its midpoint.

PARALLEL LINES

Lines in the same plane that never intersect and maintain a constant distance apart.

ANGLE

A geometric figure formed by two rays sharing a common endpoint.

VERTEX

The common endpoint from which the two rays of an angle originate.

RIGHT ANGLE

An angle that measures exactly $90^\text{o}$.

ACUTE ANGLE

An angle with a measure that is less than $90^\text{o}$.

OBTUSE ANGLE

An angle with a measure greater than $90^\text{o}$ but less than $180^\text{o}$.

STRAIGHT ANGLE

An angle that measures exactly $180^\text{o}$.

CONGRUENT ANGLES

Angles that have the exact same measure in degrees.

ADJACENT ANGLES

Two angles that share a common vertex and a common side but no interior points.

ANGLE ADDITION POSTULATE

If $D$ is in the interior of $\text{angle } ABC$, then the measure of the smaller angles equals the total: $m\text{angle } ABD + m\text{angle } DBC = m\text{angle } ABC$.

ANGLE BISECTOR

A ray that divides an angle into two smaller angles with equal measures.

VERTICAL ANGLES

A pair of opposite angles formed by intersecting lines that share a vertex and are congruent.

COMPLEMENTARY ANGLES

Two angles whose measures have a sum of exactly $90^\text{o}$.

SUPPLEMENTARY ANGLES

Two angles whose measures have a sum of exactly $180^\text{o}$.

LINEAR PAIR

Adjacent angles that form a straight line and are supplementary, summing to $180^\text{o}$.