Geometry Basics: Unit 1 Flashcards
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Questions and Answers

What is a point?

A location with no size or shape.

What is a line?

Made up of points with no thickness or width.

What is a plane?

A flat surface made up of points that extends indefinitely in all directions.

What does it mean for points to be collinear?

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

What does it mean for points to be coplanar?

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

What is a line segment?

<p>A measurable part of a line consisting of two endpoints.</p> Signup and view all the answers

What is the distance formula?

<p>Used to find the distance between 2 points on a coordinate plane.</p> Signup and view all the answers

What are congruent segments?

<p>Segments that have the same length.</p> Signup and view all the answers

What is the midpoint formula?

<p>Used to find the middle point between two endpoints.</p> Signup and view all the answers

What is a segment bisector?

<p>Any segment, line, or plane that intersects a segment at its midpoint.</p> Signup and view all the answers

What is a ray?

<p>A portion of a line that extends indefinitely in one direction.</p> Signup and view all the answers

What is an angle?

<p>The intersection of two rays at an endpoint.</p> Signup and view all the answers

What is a vertex?

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

What is a right angle?

<p>An angle that measures 90 degrees.</p> Signup and view all the answers

What is an acute angle?

<p>An angle that measures less than 90 degrees.</p> Signup and view all the answers

What is an obtuse angle?

<p>An angle that measures more than 90 degrees but less than 180 degrees.</p> Signup and view all the answers

What are congruent angles?

<p>Angles that have the same measure.</p> Signup and view all the answers

What are adjacent angles?

<p>Angles that have a common side and a common vertex.</p> Signup and view all the answers

What are vertical angles?

<p>Two angles directly across from each other on intersecting lines.</p> Signup and view all the answers

What are complementary angles?

<p>Two angles whose sum is 90 degrees.</p> Signup and view all the answers

What are supplementary angles?

<p>Two angles whose sum is 180 degrees.</p> Signup and view all the answers

What is a linear pair?

<p>Adjacent angles that are supplementary.</p> Signup and view all the answers

What does it mean for lines to be perpendicular?

<p>Two lines that intersect at a 90 degree angle.</p> Signup and view all the answers

What is an angle bisector?

<p>A line or ray that divides an angle into two congruent angles.</p> Signup and view all the answers

What are the undefined terms of geometry?

<p>Point, line, plane.</p> Signup and view all the answers

What is the segment addition postulate?

<p>If A, B, and C are collinear points and B is between A and C, then AB + BC = AC.</p> Signup and view all the answers

What is a perpendicular bisector?

<p>A line, segment, or ray that is perpendicular to the segment at its midpoint.</p> Signup and view all the answers

What are parallel lines?

<p>Two coplanar lines that never intersect.</p> Signup and view all the answers

What is a straight angle?

<p>An angle that measures 180 degrees.</p> Signup and view all the answers

What is the angle addition postulate?

<p>If angle ABD and angle DBC are adjacent, then angle ABD + angle DBC = angle ABC.</p> Signup and view all the answers

Study Notes

Basic Geometry Terms

  • Point: Represents a specific location with no dimensions; fundamental building block in geometry.
  • Line: Composed of infinitely many points extending without thickness in both directions.
  • Plane: A two-dimensional flat surface, extending infinitely in all directions, formed by points.

Collinearity and Coplanarity

  • Collinear Points: A set of points that all lie on a single straight line.
  • Coplanar Points: Points that reside within the same flat surface (plane).

Line Segments and Distances

  • Line Segment: A measurable portion of a line defined by two endpoints.
  • Distance Formula: A mathematical equation used to determine the distance between two points in a coordinate plane.

Congruence and Midpoints

  • Congruent Segments: Line segments that are equal in length.
  • Midpoint Formula: A formula for locating the exact middle point of a line segment defined by two endpoints.

Segment and Angle Definitions

  • Segment Bisector: Any line, ray, or plane that crosses a line segment at its midpoint.
  • Ray: A part of a line that has one endpoint and extends infinitely in the other direction.

Angles and Their Properties

  • Angle: Formed by the intersection of two rays that share a common endpoint, called the vertex.
  • Vertex: The shared endpoint of the rays that form an angle.
  • Right Angle: An angle that measures exactly 90 degrees.
  • Acute Angle: An angle that measures less than 90 degrees.
  • Obtuse Angle: An angle measuring more than 90 degrees but less than 180 degrees.

Angle Relationships

  • Congruent Angles: Angles that have identical measures.
  • Adjacent Angles: Angles that share a side and a vertex, positioned next to each other.
  • Vertical Angles: Angles positioned directly across from one another when two lines intersect.
  • Complementary Angles: Two angles whose measures add up to 90 degrees.
  • Supplementary Angles: Two angles whose measures total 180 degrees.
  • Linear Pair: A set of adjacent angles that form a straight line and are supplementary.

Special Angle Relationships

  • Perpendicular Lines: Two lines that intersect to form right angles (90 degrees).
  • Angle Bisector: A line or ray that divides an angle into two equal angles.

Undefined Terms and Postulates

  • Undefined Terms: Basic concepts in geometry include point, line, and plane, which are not formally defined.
  • Segment Addition Postulate: States that if point B lies between points A and C, the sum of the segments AB and BC will equal segment AC.
  • Perpendicular Bisector: A segment or line that divides another segment into two equal parts at a right angle.
  • Parallel Lines: Coplanar lines that do not meet or intersect at any point.

Angle Measures

  • Straight Angle: An angle that measures exactly 180 degrees.
  • Angle Addition Postulate: States that the sum of two adjacent angles equals the measure of their combined angle.

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Description

Explore the foundational concepts of geometry with these flashcards from Unit 1 of the All Things Algebra curriculum. Learn key terms like point, line, plane, and collinear through concise definitions and descriptions. Perfect for students looking to reinforce their understanding of geometric principles.

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