Geometry Unit 1: Measurements and Proof Flashcards

Vocabulary flashcards covering fundamental geometric terms, measurement postulates, logic, and proof properties as presented in the Unit 1 lecture notes.

Point

One of the three undefined terms in geometry used to represent a specific location.

Line

An undefined term in geometry that extends infinitely in two directions.

Plane

An undefined term in geometry representing a flat, two-dimensional surface.

Line Segment

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

Ray

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

Parallel Lines

Lines in the same plane that never intersect.

Perpendicular Lines

Lines that intersect to form right angles.

Skew Lines

Lines that are not in the same plane and do not intersect.

Adjacent Angles

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

Complementary Angles

Two angles whose measures have a sum of $90^{\circ}$.

Supplementary Angles

Two angles whose measures have a sum of $180^{\circ}$.

Linear Pair

A pair of adjacent angles whose non-common sides are opposite rays, forming a straight line.

Vertical Angles

The non-adjacent angles formed by two intersecting lines.

Convex Polygon

A polygon where no part of a diagonal contains points in the exterior of the polygon.

Concave Polygon

A polygon that has at least one diagonal with points in the exterior of the polygon.

Regular Polygon

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

Circumference

The linear distance around the outside of a circle.

Collinear Points

Points that lie on the same line.

Coplanar Points

Points that lie on the same plane.

Segment Addition Postulate

The principle stating that if point B is between points A and C, then $AB + BC = AC$.

Midpoint formula

The formula used to find the center of a segment: $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$.

Distance Formula

An algebraic formula used to find the length between two points: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Protractor Postulate

The postulate that allows every angle to be measured between $0^{\circ}$ and $180^{\circ}$.

Angle Addition Postulate

The principle stating that if D is in the interior of $\angle ABC$, then $m\angle ABD + m\angle CBD = m\angle ABC$.

Obtuse angle

An angle whose measure is greater than $90^{\circ}$ but less than $180^{\circ}$.

Acute angle

An angle whose measure is less than $90^{\circ}$.

Right angle

An angle whose measure is exactly $90^{\circ}$.

Straight angle

An angle whose measure is exactly $180^{\circ}$.

Conditional Statement

A logical statement written in the form "If p, then q," symbolized as $p \rightarrow q$.

Converse

A statement formed by switching the hypothesis and the conclusion: $q \rightarrow p$.

Inverse

A statement formed by negating both the hypothesis and the conclusion: $\neg p \rightarrow \neg q$.

Contrapositive

A statement formed by negating and switching both the hypothesis and the conclusion: $\neg q \rightarrow \neg p$.

Biconditional Statement

A statement that contains the phrase "if and only if," which is true when both the conditional and its converse are true.

Inductive Reasoning

The process of reaching a conclusion based on patterns, observations, or specific examples.

Deductive Reasoning

The process of reaching a conclusion based on facts, definitions, properties, or laws of logic.

Law of Detachment

A law of logic stating that if $p \rightarrow q$ is true and $p$ is true, then $q$ must also be true.

Law of Syllogism

A law of logic stating that if $p \rightarrow q$ and $q \rightarrow r$ are true, then $p \rightarrow r$ is also true.

Reflexive Property

The property stating that a value is equal to itself: $a = a$.

Symmetric Property

The property stating that if $a = b$, then $b = a$.

Transitive Property

The property stating that if $a = b$ and $b = c$, then $a = c$.

Substitution Property

The property of equality stating that if $a = b$, then $a$ may be replaced by $b$ in any expression or equation.

Vertical Angles Theorem

A theorem stating that vertical angles are always congruent ($\angle 1 \cong \angle 2$).