Vocabulary_Terms_-_PDF_2025-01-29_16_56_48
Geometry Vocabulary
Radical
The symbol used to denote the nth root.
Radicand
The expression under (or inside) the radical.
Index
Number indicating which root to take (e.g., index 2 for square root).
Example: √25 indicates that 5 is the square root since the index is understood as 2.
Chapter 1 – The Fundamentals
Postulate
A statement accepted to be true without proof.
Theorem
A statement that has been proven and is accepted as truth.
Point
A location; has no shape or size.
Line
A set of points extending indefinitely in two directions; has length but no thickness.
Segment
A part of a line consisting of two endpoints and all points between.
AC
The distance between points A and C; measure of length.
Between
Point B is between A and C if A, B, and C are collinear, and AB + BC = AC.
Segment Addition Postulate
If B is between A and C, then AB + BC = AC.
Midpoint
A point halfway between endpoints; K is the midpoint of J and L if K is between J and L and JK = KL.
Segment Bisector
A line, ray, or plane that intersects a segment at its midpoint.
Ray
A part of a line with one endpoint extending indefinitely in one direction.
Opposite Rays
Rays sharing an endpoint and extending in opposite directions.
Plane
A flat surface extending indefinitely in all directions; has length and width, but no depth.
Intersection
The set of points that figures have in common.
Collinear
Points lying on the same line.
Coplanar
Points lying in the same plane.
Space
A boundless three-dimensional set of all points.
Chapter 2 – Reasoning & Proof
Inductive Reasoning
Reasoning using specific examples and patterns to reach a conclusion.
Conjecture
An educated guess based on known information; a conclusion from inductive reasoning.
Statement
A sentence either true or false.
Truth Value
The truth or falsity of a statement.
Counterexample
An example showing that a statement is false.
Conjunction
A compound statement using "and" to join two or more statements.
Disjunction
A compound statement using "or" to join statements.
Negation
A statement with the opposite meaning and truth value.
Tautology
A statement that is always true.
Contradiction
A statement that is always false.
Conditional Statement
A statement in if-then form.
Hypothesis
The part of an if-then statement after "if".
Conclusion
The part of an if-then statement after "then".
Converse
A statement formed by switching the hypothesis and conclusion.
Inverse
A statement formed by negating both the hypothesis and conclusion.
Contrapositive
A statement formed by negating the converse.
Deductive Reasoning
Reasoning using facts to reach a logical conclusion.
Law of Detachment
If p → q is true and p is true, then q is true.
Law of Syllogism
If p → q is true, and q → r is true, then p → r is true.
Proof
A logical argument supported by definitions, properties, postulates, theorems, or corollaries.
Chapter 3 – Angle & Line Relationships
Parallel Lines
Coplanar lines that do not intersect (denoted by ( || )).
Skew Lines
Non-coplanar lines that are non-parallel and do not intersect.
Transversal
A line that intersects two or more lines.
Alternate Interior Angles
Angles on opposite sides of the transversal between intersected lines.
Alternate Exterior Angles
Angles on opposite sides of the transversal outside of the intersected lines.
Consecutive Interior Angles
Angles on the same side of the transversal between intersected lines.
Corresponding Angles
Angles in the same position relative to the transversal and each intersected line.
Slope
A number measuring the steepness of a line.
Exterior Angle
An angle formed by a side and the extension of an adjacent side.
Remote Interior Angles
The two non-adjacent interior angles for an exterior angle of a triangle.
Chapter 4 – Triangle Basics
Types of Triangles:
Acute Triangle: All angles < 90°.
Right Triangle: Exactly one angle = 90°.
Obtuse Triangle: Exactly one angle > 90°.
Equiangular Triangle: All angles equal.
Scalene Triangle: No equal sides.
Isosceles Triangle: At least two equal sides.
Equilateral Triangle: All sides equal.
Hypotenuse
The side opposite the right angle in a right triangle.
Legs
The congruent sides of an isosceles triangle.
Base
The remaining side of an isosceles triangle.
Vertex Angle
The angle formed by congruent sides in an isosceles triangle.
Base Angles
Angles formed by each leg and the base of an isosceles triangle.
Theorems:
The sum of the angle measures of a triangle is 180°.
Base angles of an isosceles triangle are congruent.
Chapter 5 – Triangles: A Closer Look
Concurrent Lines
Three or more lines intersecting at a common point.
Point of Concurrency
The intersection of three or more lines.
Median of a Triangle
A segment from a vertex to the midpoint of the opposite side.
Altitude
A segment from a vertex that is perpendicular to the opposite side.
Incenter
The intersection of the angle bisectors of a triangle.
Centroid
The intersection of the medians of a triangle.
Circumcenter
The intersection of the perpendicular bisectors of a triangle.
Orthocenter
The intersection of the altitudes of a triangle.
Midsegment
A segment joining the midpoints of the sides of a triangle.
Chapter 6 - Similarity
Ratio
Comparison of two numbers by division.
Proportion
An equation stating two ratios are equal.
Similar Figures
Figures with the same shape that are proportional in size.
Scale Factor
The ratio of corresponding parts.
Chapter 7 – Right Triangles & Basic Trigonometry
Geometric Mean
A positive number x such that a:x as x:b.
Pythagorean Theorem
In a right triangle: (side1)² + (side2)² = (hypotenuse)².
Pythagorean Triple
Three whole numbers satisfying the Pythagorean Theorem.
Trigonometry
The study of triangles.
Trigonometric Ratios:
Sine: Opposite side / Hypotenuse.
Cosine: Adjacent side / Hypotenuse.
Tangent: Opposite side / Adjacent side.
Angle of Elevation
The angle formed by the line of sight and the horizontal, looking upward.
Angle of Depression
The angle formed by the line of sight and the horizontal, looking downward.
Chapter 8 – Polygons & Quadrilaterals
n-gon
A polygon with "n" sides.
Quadrilateral
A polygon with exactly four sides.
Types of Quadrilaterals:
Parallelogram: Two pairs of parallel sides.
Rectangle: Four right angles.
Rhombus: Four congruent sides.
Square: Four right angles and four congruent sides.
Trapezoid: Exactly one pair of parallel sides.
Isosceles Trapezoid: One pair of parallel sides and one pair of congruent sides.
Median of a Trapezoid: A segment whose endpoints are midpoints of the legs.
Kite: Two pairs of congruent consecutive sides; opposite sides are not parallel.
Chapter 9 - Circles
Circle
Set of points in a plane equidistant from a center point.
Chord
A segment with both endpoints on the circle.
Radius
Segment from the center to a point on the circle.
Diameter
A chord passing through the center.
Pi (π)
Ratio of circumference to diameter.
Arc
A piece of a circle between two endpoints.
Minor Arc
Arc measuring < 180°.
Major Arc
Arc measuring > 180°.
Semicircle
Arc measuring 180°.
Central Angle
An angle whose vertex is at the center of the circle.
Inscribed Angle
An angle with vertex on the circle; sides are chords.
Tangent Line
A line intersecting a circle at exactly one point.
Secant Line
A line intersecting a circle at exactly two points.
Chapter 10 - Area, Surface Area, & Volume
Apothem
Segment from the center forming a right angle with a side of a regular polygon.
Sector of a Circle
A region bounded by a central angle and the arc.
Segment of a Circle
A region bounded by an arc and a chord.
Solid
A three-dimensional figure.
Polyhedron
A solid with all flat surfaces enclosing a single space.
Prism
A polyhedron with two parallel, congruent faces.
Pyramid
A polyhedron with one vertex connecting at the top.
Cylinder
Solid with congruent circular bases in parallel planes.
Cone
Solid with a circular base and vertex not in the same plane.
Sphere
Set of points equidistant from a center point.
Surface Area
Sum of the areas of each face of a solid.
Volume
Amount of space enclosed by a solid.
Geometry Vocabulary Flashcards
Radical: The symbol used to denote the nth root.
Radicand: The expression under (or inside) the radical.
Index: Number indicating which root to take (e.g., index 2 for square root). Example: √25 indicates that 5 is the square root since the index is understood as 2.
Chapter 1 – The Fundamentals Flashcards
Postulate: A statement accepted to be true without proof.
Theorem: A statement that has been proven and is accepted as truth.
Point: A location; has no shape or size.
Line: A set of points extending indefinitely in two directions; has length but no thickness.
Segment: A part of a line consisting of two endpoints and all points between.
AC: The distance between points A and C; measure of length.
Between: Point B is between A and C if A, B, and C are collinear, and AB + BC = AC.
Segment Addition Postulate: If B is between A and C, then AB + BC = AC.
Midpoint: A point halfway between endpoints; K is the midpoint of J and L if K is between J and L and JK = KL.
Segment Bisector: A line, ray, or plane that intersects a segment at its midpoint.
Ray: A part of a line with one endpoint extending indefinitely in one direction.
Opposite Rays: Rays sharing an endpoint and extending in opposite directions.
Plane: A flat surface extending indefinitely in all directions; has length and width, but no depth.
Intersection: The set of points that figures have in common.
Collinear: Points lying on the same line.
Coplanar: Points lying in the same plane.
Space: A boundless three-dimensional set of all points.