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?
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What does it mean for points to be coplanar?
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What is a line segment?
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What is the distance formula?
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What are congruent segments?
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What is the midpoint formula?
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What is a segment bisector?
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What is a ray?
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What is an angle?
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What is a vertex?
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What is a right angle?
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What is an acute angle?
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What is an obtuse angle?
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What are congruent angles?
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What are adjacent angles?
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What are vertical angles?
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What are complementary angles?
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What are supplementary angles?
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What is a linear pair?
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What does it mean for lines to be perpendicular?
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What is an angle bisector?
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What are the undefined terms of geometry?
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What is the segment addition postulate?
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What is a perpendicular bisector?
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What are parallel lines?
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What is a straight angle?
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What is the angle addition postulate?
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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.