Geometry - 01.01 Lesson Flashcards
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Questions and Answers

What are undefined terms in geometry?

Basic figures that are not defined in terms of other figures; they include point, line, and plane.

What are defined terms in geometry?

Explained using undefined terms and/or other defined terms.

What is a point?

A location in space that is represented by a dot and has no dimension.

How are points named?

<p>Points are named using a capital letter.</p> Signup and view all the answers

What is a line?

<p>A straight path that has no thickness and extends forever.</p> Signup and view all the answers

How many dimensions does a line have?

<p>1 dimension: length.</p> Signup and view all the answers

How are lines named?

<p>Using two or more points on the line or a lowercase script letter.</p> Signup and view all the answers

What are collinear points?

<p>Points that lie on the same line.</p> Signup and view all the answers

What are noncollinear points?

<p>Points that do not lie on the same line.</p> Signup and view all the answers

What is a plane?

<p>A flat surface that extends indefinitely in all directions.</p> Signup and view all the answers

How many dimensions does a plane have?

<p>2 dimensions: length and width.</p> Signup and view all the answers

How is a plane named?

<p>By a single letter or three coplanar, non-collinear points.</p> Signup and view all the answers

How is a plane drawn?

<p>As a four-sided figure resembling a tabletop or a parallelogram.</p> Signup and view all the answers

What are coplanar points?

<p>Points that lie on the same plane.</p> Signup and view all the answers

What are noncoplanar points?

<p>Points that do not lie on the same plane.</p> Signup and view all the answers

What does geometry mean?

<p>It means 'earth measuring'.</p> Signup and view all the answers

What is a line segment?

<p>A portion of a line with two endpoints.</p> Signup and view all the answers

What is a ray?

<p>A ray has one endpoint and continues indefinitely in one direction.</p> Signup and view all the answers

What is a vertex?

<p>The common endpoint of the two rays in an angle.</p> Signup and view all the answers

What constitutes an angle?

<p>Two rays with a common endpoint that separate a plane into two parts.</p> Signup and view all the answers

What defines a circle?

<p>All of the points on the circle are a given distance from a given point (the center).</p> Signup and view all the answers

What is a postulate?

<p>A piece of information accepted as a fact, which does not need to be proven.</p> Signup and view all the answers

What is a theorem?

<p>Any statement that you can prove.</p> Signup and view all the answers

What can be used to prove theorems true?

<p>Postulates, definitions, and undefined terms.</p> Signup and view all the answers

Study Notes

Undefined and Defined Terms

  • Undefined terms are basic figures not defined by other figures; key undefined terms are point, line, and plane.
  • Defined terms are explained using undefined terms or other defined terms.

Points

  • A point represents a location in space and has no dimension (size).
  • Points are named using capital letters, e.g., Point A or Point X.

Lines

  • A line is an undefined term characterized as a straight path with no thickness, extending infinitely.
  • A line has one dimension: length.
  • Lines are named by two or more points on the line or a lowercase script letter (e.g., line m or line AD).

Collinear and Noncollinear Points

  • Collinear points lie on the same line, indicated by the prefix "co-" (together) and "linear" (line).
  • Noncollinear points do not lie on the same line.

Planes

  • A plane is a flat surface extending indefinitely in all directions.
  • A plane has two dimensions: length and width.
  • It's named by a single letter (e.g., plane m) or three non-collinear points (e.g., plane ABC).

Points in Relation to Planes

  • Coplanar points lie on the same plane.
  • Noncoplanar points do not lie on the same plane.

Geometry

  • The term geometry derives from "geo" (earth) and "metri" (to measure), meaning "earth measuring."

Line Segments and Rays

  • A line segment is a defined term with two endpoints, containing all points between them.
  • A ray has one endpoint and extends infinitely in one direction.

Angles

  • An angle comprises two rays with a common endpoint, separating a plane into interior and exterior parts.
  • Angles are named by placing the vertex between two letters (e.g., ∠ABC) or just naming the vertex (e.g., ∠B).

Circles

  • All points on a circle are at a fixed distance (radius) from a center point.

Postulates and Theorems

  • Postulates are accepted facts that do not need proof (e.g., two distinct points determine a unique line).
  • Theorems are statements that can be proven using postulates and definitions; they must be demonstrated rather than assumed.

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Test your knowledge on the basic concepts of geometry with these flashcards. This quiz covers undefined and defined terms, which are essential for understanding geometric principles. Perfect for students seeking to solidify their foundational knowledge in geometry.

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