Geometry Basics, Angles, Lines, and Reasoning

Vocabulary flashcards covering geometry basics, angles, lines, and fundamental logic and reasoning terms.

Point

A precise location in space represented by a dot (has no size).

Line

A straight path of points that extends infinitely in two opposite directions ($\overleftrightarrow{AB}$).

Plane

A flat, 2D surface that extends infinitely in all directions.

Collinear Points

Points that lie on the exact same line.

Coplanar Points

Points or lines that lie in the exact same plane.

Line Segment

A part of a line bounded by two distinct endpoints ($\overline{AB}$).

Ray

A part of a line with one endpoint that extends infinitely in one direction ($\overrightarrow{AB}$).

Intersection

The point or set of points where two geometric figures meet (two lines intersect at a point; two planes intersect at a line).

Segment Addition Postulate

If B is between A and C, then $AB + BC = AC$.

Congruent Segments

Line segments that have the exact same length.

Midpoint

A point that divides a line segment into two equal (congruent) halves.

Segment Bisector

A line, ray, or segment that passes through the midpoint of a segment, cutting it in half.

Distance Formula

Derived from Pythagorean theorem: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Midpoint Formula

$$\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$

Vertex

The common endpoint where two rays meet to form an angle.

Angle Addition Postulate

If point B lies in the interior of $\angle AOC$, then $m\angle AOB + m\angle BOC = m\angle AOC$.

Acute Angle

An angle measuring less than $90^\circ$.

Right Angle

An angle measuring exactly $90^\circ$.

Obtuse Angle

An angle measuring greater than $90^\circ$ but less than $180^\circ$.

Straight Angle

An angle measuring exactly $180^\circ$ (a straight line).

Congruent Angles

Angles that have the exact same degree measure.

Angle Bisector

A ray or line that divides an angle into two equal (congruent) angles.

Adjacent Angles

Two angles that share a common vertex and side, but do not overlap.

Complementary Angles

Two angles whose measures add up to $90^\circ$ ($a + b = 90^\circ$).

Supplementary Angles

Two angles whose measures add up to $180^\circ$ ($a + b = 180^\circ$).

Linear Pair

Two adjacent angles whose non-shared sides form a straight line (they are always supplementary = $180^\circ$).

Vertical Angles

Opposite angles formed by two intersecting lines; they are always congruent ($\angle 1 \cong \angle 2$).

Perpendicular Lines

Two lines that intersect to form $90^\circ$ right angles.

Perpendicular Bisector

A line perpendicular to a segment that cuts it into two equal halves at its midpoint.

Inductive Reasoning

Making conclusions based on patterns or observations.

Deductive Reasoning

Using facts, rules, definitions, or logic to prove a statement.

Postulate / Axiom

A rule or statement accepted as true without proof.

Theorem

A statement that has been proven true using logic and postulates.