Geometry Undefined Terms Flashcards

Questions and Answers

What is the definition of an undefined term?

A term that includes a point, a line, and a plane. (correct)

A term that is formally defined. (correct)

A term explained using either undefined terms or other defined terms.

A term that has size and shape.

What does a point not have?

Size or shape.

What is a line?

An infinite set of points extending forever in each direction.

Describe a plane.

A flat two-dimensional surface that extends infinitely. Signup and view all the answers

What is space defined as?

The set of all points. Signup and view all the answers

What are defined terms?

Terms explained using undefined terms or other defined terms. Signup and view all the answers

Collinear points lie on the same line.

True Signup and view all the answers

Noncollinear points lie on the same line.

False Signup and view all the answers

What does coplanar refer to?

Objects lying on the same plane. Signup and view all the answers

Noncoplanar objects lie on the same plane.

False Signup and view all the answers

What is the intersection of figures?

The set of points that two or more figures have in common. Signup and view all the answers

Parallel lines intersect.

False Signup and view all the answers

What is a postulate?

A statement accepted as true without proof. Signup and view all the answers

What is the postulate for a plane?

Exactly one plane through 3 noncollinear points. Signup and view all the answers

Study Notes

Undefined Terms in Geometry

Undefined terms are foundational concepts not formally defined but fundamental to understanding geometry.
Key undefined terms include point, line, and plane.

Point

Represents a specific location in space.
Lacks size and shape, serving as a fundamental building block in geometry.

Line

Composed of an infinite set of points extending indefinitely in both directions.
Has no thickness or width, providing a one-dimensional representation.

Plane

Defines a flat two-dimensional surface that extends infinitely in all directions.
Lacks thickness, allowing for the representation of flat shapes and figures.

Space

Encompasses the entirety of points within a geometric context.

Defined Terms

These terms are explained using undefined terms or other defined terms to clarify meanings.

Collinear Points

Describes a scenario where two or more points reside on the same straight line.

Noncollinear Points

Refers to two or more points that do not fall on the same straight line.

Coplanar Objects

Indicates when objects or points exist on the same two-dimensional plane.

Noncoplanar Objects

Describes situations where objects or points do not share the same plane.

Intersection

Represents the set of points shared by two or more geometric figures.

Parallel Lines

Defined as coplanar lines that remain equidistant from one another and do not meet.

Postulates

Refer to axioms or statements accepted as true without requiring proof.
In geometry, postulates serve as foundational principles for theorems and proofs.

Postulates for Plane

There exists exactly one plane through any three noncollinear points.
A plane must contain at least three noncollinear points.
If two points are part of a plane, the line connecting them also lies within that plane.

Description

Test your knowledge of fundamental geometric concepts with these flashcards on undefined terms. Learn about the definitions of a point, line, and plane, which are essential in the study of geometry. Perfect for quick revision or preparation for exams!