Geometry Vocabulary: Basic Concepts, Proofs, and Congruent Triangles

Comprehensive vocabulary flashcards covering basic geometric definitions, proof terminology, logic, angle classifications, and triangle congruence shortcuts.

Angle

A geometric figure made up of two rays that share a common endpoint called the vertex.

Vertex

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

Acute Angle

An angle whose measure is greater than $0^{\circ}$ and less than $90^{\circ}$.

Right Angle

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

Obtuse Angle

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

Straight Angle

An angle whose measure is exactly $180^{\circ}$, forming a straight line.

Congruent Angles

Angles that have the exact same measure.

Congruent Segments

Line segments that have the exact same length.

Collinear Points

Points that lie on the same straight line.

Noncollinear Points

Points that do not all lie on the same straight line.

Theorem

A mathematical statement that can be proved using logical reasoning, postulates, and definitions.

Midpoint

The point on a segment that divides it into two congruent segments.

Segment Bisector

A point, line segment, ray, or line that intersects a segment at its midpoint, dividing it into two congruent segments.

Trisection Points

Two points that divide a segment into three congruent segments.

Angle Bisector

A ray that divides an angle into two congruent angles.

Angle Trisectors

Two rays that divide an angle into three congruent angles.

Deductive Structure

A system of thought in which conclusions are justified by means of previously assumed or proved statements (undefined terms, postulates, definitions, and theorems).

Postulate

An unproved assumption accepted as true.

Definition

A formal statement that states the precise meaning of a term or idea and is always reversible.

Conditional Statement

An "If…, then…" statement symbolized as $p \Rightarrow q$.

Hypothesis

The clause following the word "if" in a conditional statement ($p$).

Conclusion (Logic)

The clause following the word "then" in a conditional statement ($q$).

Converse

A statement formed by reversing the hypothesis and conclusion of a conditional statement ("If $q$, then $p$").

Negation

The statement "not $p$" (symbolized as $\sim p$), which expresses the opposite truth value of statement $p$.

Inverse

A statement formed by negating both the hypothesis and conclusion of a conditional statement ("If $\sim p$, then $\sim q$").

Contrapositive

A statement formed by negating and reversing both the hypothesis and conclusion of a conditional statement ("If $\sim q$, then $\sim p$").

Perpendicular Lines

Lines, rays, or segments that intersect to form right angles ($90^{\circ}$).

Oblique Lines

Lines that intersect but are not perpendicular.

Complementary Angles

Two angles whose sum is $90^{\circ}$ (a right angle).

Supplementary Angles

Two angles whose sum is $180^{\circ}$ (a straight angle).

Opposite Rays

Two collinear rays that share a common endpoint and extend infinitely in opposite directions.

Vertical Angles

Two nonadjacent angles formed by two intersecting lines whose sides form pairs of opposite rays.

Congruent Triangles

Triangles in which all pairs of corresponding sides and corresponding angles are congruent.

Reflexive Property

A property stating that any geometric figure (segment, angle, or shape) is congruent to itself.

SSS Postulate

If three sides of one triangle are congruent to three sides of another triangle, the two triangles are congruent.

SAS Postulate

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the two triangles are congruent.

ASA Postulate

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent.

CPCTC

An abbreviation for "Corresponding Parts of Congruent Triangles are Congruent."

Radius

A line segment extending from the center of a circle to any point on the circle itself.

Median of a Triangle

A line segment drawn from any vertex of a triangle to the midpoint of the opposite side.

Altitude of a Triangle

A line segment drawn from any vertex of a triangle perpendicular to the line containing the opposite side.

Auxiliary Line

A line, ray, or segment added to a geometric diagram to help construct a proof.

Scalene Triangle

A triangle in which no two sides are congruent.

Isosceles Triangle

A triangle in which at least two sides are congruent.

Equilateral Triangle

A triangle in which all three sides are congruent.

Equiangular Triangle

A triangle in which all three angles are congruent.

Acute Triangle

A triangle in which all three angles are acute ($< 90^{\circ}$).

Right Triangle

A triangle that contains one right angle ($90^{\circ}$).

Obtuse Triangle

A triangle that contains one obtuse angle ($> 90^{\circ}$).

HL Postulate

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, the two right triangles are congruent.