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All courses Geometry · G-CO.1 1 of 57
Use precise definitions of angle, circle, perpendicular line, parallel line, and line segment from point/line/distance ideas.

Identify a plane from a geometric description

Problem
Identify the geometric object described by a flat surface extending without end through points \(A\), \(B\), and \(C\).
Clean labeled source geometry diagram without the requested classification or definition. Open full size
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Hint

Focus on the phrase \(flat surface extending without end\) before deciding which object it names.

A plane is a flat surface that extends forever in all directions within the surface. Three points like \(A\), \(B\), and \(C\) can name a plane.

Solution walkthrough

01

Decode the dimensional description

\[\text{flat}~\text{surface}~\text{extending}~\text{without}~\text{end}~->~\text{plane}\]

A plane is a flat two-dimensional surface extending infinitely, unlike a line or finite polygon.

02

Inspect the naming points

\[A,~B,~C~\text{lie}~\text{on}~\text{the}~\text{displayed}~\text{plane}\]

The inspected diagram places three labeled noncollinear points on the shaded plane representation.

03

Apply plane naming convention

\[\text{three}~\text{noncollinear}~\text{points}~A,B,C~->~\text{plane}~ABC\]

A plane can be named by three noncollinear points that lie on it. The drawn parallelogram is only a finite visual symbol for the infinite plane.

04

State the exact object

\[\text{plane}~ABC\]

The described infinite flat surface through the three points is plane ABC.

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Another way

  1. Eliminate point, line, ray, and segment by dimension and extent, leaving a plane.

!

Common mistake

Do not call the object a parallelogram. The diagram's boundary is a drawing convention; the stated plane extends without end.

Annotated answer diagram with the precise geometric definition or classification.
object: plane ABC

Solution walkthrough video