Geometry Basics: Unit 1 Flashcards

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?

Points that lie on the same line. Signup and view all the answers

What does it mean for points to be coplanar?

Points that lie on the same plane. Signup and view all the answers

What is a line segment?

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

What is the distance formula?

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

What are congruent segments?

Segments that have the same length. Signup and view all the answers

What is the midpoint formula?

Used to find the middle point between two endpoints. Signup and view all the answers

What is a segment bisector?

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

What is a ray?

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

What is an angle?

The intersection of two rays at an endpoint. Signup and view all the answers

What is a vertex?

The common endpoint of an angle. Signup and view all the answers

What is a right angle?

An angle that measures 90 degrees. Signup and view all the answers

What is an acute angle?

An angle that measures less than 90 degrees. Signup and view all the answers

What is an obtuse angle?

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

What are congruent angles?

Angles that have the same measure. Signup and view all the answers

What are adjacent angles?

Angles that have a common side and a common vertex. Signup and view all the answers

What are vertical angles?

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

What are complementary angles?

Two angles whose sum is 90 degrees. Signup and view all the answers

What are supplementary angles?

Two angles whose sum is 180 degrees. Signup and view all the answers

What is a linear pair?

Adjacent angles that are supplementary. Signup and view all the answers

What does it mean for lines to be perpendicular?

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

What is an angle bisector?

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

What are the undefined terms of geometry?

Point, line, plane. Signup and view all the answers

What is the segment addition postulate?

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

What is a perpendicular bisector?

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

What are parallel lines?

Two coplanar lines that never intersect. Signup and view all the answers

What is a straight angle?

An angle that measures 180 degrees. Signup and view all the answers

What is the angle addition postulate?

If angle ABD and angle DBC are adjacent, then angle ABD + angle DBC = angle ABC. 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.