Geometry Chapter 1 Vocabulary

Flashcards covering geometric terms, definitions, transformation types, angle classifications, and probability concepts from Chapter 1 notes.

Investigative Process

A process used to study and learn new mathematical ideas that follows the sequence of asking a question, exploring and forming a conjecture, and proving the conjecture.

Conjecture

An educated guess or mathematical statement that has not yet been proven.

Proof

A convincing logical argument that uses definitions and previously proven conjectures in an organized sequence.

Acute Angle

Any angle with a measure between (but not including) $0^\times$ and $90^\times$.

Right Angle

Any angle that measures exactly $90^\times$.

Obtuse Angle

Any angle with a measure between (but not including) $90^\times$ and $180^\times$.

Straight Angle

An angle that measures $180^\times$ and is formed when the sides of the angle form a straight line.

Circular Angle

Any angle that measures exactly $360^\times$.

Rigid Transformation

A function that assigns each point in the plane to a unique point in the plane, preserving angles and distances so that the resulting image has the same size and shape as the original.

Translation

A rigid transformation that slides a figure to a new location while preserving its size, shape, and orientation, such that all line segments connecting original points to their image points are parallel and equal in length.

Reflection

A rigid transformation that flips a figure across a line to form a mirror image, where the line of reflection is the perpendicular bisector of the segments connecting original points to their image points.

Line of Reflection

The mirror line across which a figure is flipped during a reflection; it serves as the perpendicular bisector of the segments connecting the original points to their corresponding image points.

Rotation

A rigid transformation that turns an entire figure about a fixed point (center of rotation) through a specified angle of rotation.

Prime Notation

A labeling system using prime symbols (such as $A'$) to mark the image points of a transformation and show exact correspondence to the original shape's points.

Slope

The ratio of the change in $y$ (\text{\Delta} y) to the change in $x$ (\text{\Delta} x) between any two points on a line, represented as \text{slope} = \frac{\text{vertical change}}{\text{horizontal change}} = \frac{\text{\Delta} y}{\text{\Delta} x}.

Parallel Lines

Lines that lie in the same plane and never intersect, having equal steepness and equal slopes.

Perpendicular Lines

Lines that intersect at a right angle ($90^\times$) and have slopes that are opposite reciprocals.

Opposite Reciprocals

Two numbers whose product is $-1$ (for example, $\frac{a}{b}$ and $-\frac{b}{a}$), describing the mathematical relationship between the slopes of perpendicular lines.

Event

Any outcome, or set of outcomes, from a probabilistic situation.

Sample Space

All possible outcomes from a probabilistic situation.

Experimental Probability

Probability based on data collected in experiments, calculated as $\text{experimental probability} = \frac{\text{number of successful outcomes in the experiment}}{\text{total number of outcomes in the experiment}}$.

Theoretical Probability

Probability that is mathematically calculated when each outcome in the sample space has an equally likely chance of occurring, calculated as $\text{theoretical probability} = \frac{\text{number of successful outcomes}}{\text{total number of outcomes}}$.

Polygon

A two-dimensional closed figure made up of straight line segments connected end-to-end that do not cross or intersect at any other points.

Regular Polygon

A polygon whose sides are all the same length and whose angles all have equal measure.

Equilateral Triangle

A triangle with three sides of equal length and three equal angles.

Scalene Triangle

A triangle in which no sides have the same length.

Isosceles Triangle

A triangle that has at least two sides of equal length.

Venn Diagram

A tool used to classify objects, usually composed of two or more overlapping circles representing different conditions.

Reflection Symmetry

A property of a figure if a reflection across a line carries the figure onto itself.

Rotation Symmetry

A property of a figure if it can be rotated about a point by an angle less than $360^\times$ and remain unchanged.

Even Function

A function whose graph has reflection symmetry across the y-axis.

Odd Function

A function whose graph has rotation symmetry about the origin $(0,0)$.