Questions and Answers
What are defined terms?
What are undefined terms?
What is a line?
What is a plane?
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What does collinear mean?
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What does coplanar mean?
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What are opposite rays?
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What is a postulate?
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What is a theorem?
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What is the congruent symbol?
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What is absolute value?
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What is the midpoint formula?
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What is the Pythagorean theorem?
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What is the distance formula?
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What is a convex polygon?
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What is a concave polygon?
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What are polygons?
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What are complementary angles?
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What are supplementary angles?
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What are adjacent angles?
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What are nonadjacent angles?
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What is a linear pair?
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What are vertical angles?
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Study Notes
Defined and Undefined Terms
- Defined terms can be described using known words, facilitating easier communication and understanding in geometry.
- Undefined terms lack formal definitions but have agreed-upon meanings within the context of geometry.
Geometry Basics
- A line is a one-dimensional figure that extends infinitely in both directions.
- A plane is a flat, two-dimensional surface that extends infinitely in all directions.
Points and Positions
- Collinear points lie on the same straight line, indicating their linear relationship.
- Coplanar points exist within the same plane, showing they share a single flat surface.
Rays and Angles
- Opposite rays are two rays that have a common endpoint and extend infinitely in opposite directions.
- Complementary angles are two angles whose measurements sum to 90 degrees, with each angle serving as the complement of the other.
- Supplementary angles have a total measurement of 180 degrees, where each angle is the supplement of the other.
- Adjacent angles share a common vertex and side but do not overlap interiorly.
- Nonadjacent angles do not share a common side or vertex and are separate from each other.
- A linear pair consists of two adjacent angles that are supplementary.
- Vertical angles are formed by the intersection of two lines, creating pairs of opposite angles.
Key Geometric Concepts
- A postulate is a rule accepted without proof, serving as a foundational concept in geometry.
- A theorem is a rule or statement that can be proven based on previously established statements or axioms.
Symbols and Formulas
- The congruent symbol indicates that two figures or angles are equal in measure.
- Absolute value represents the distance of a number from zero, always yielding a positive result.
- The midpoint formula calculates the point that is exactly halfway between two endpoints in a coordinate plane.
Theorems and Formulas
- The Pythagorean theorem relates the lengths of the sides of a right triangle, stating that (a^2 + b^2 = c^2).
- The distance formula calculates the distance between two points in a plane based on their coordinates.
Polygons and Angles
- A convex polygon has all interior angles less than 180 degrees and all vertices pointing outward.
- A concave polygon contains at least one interior angle greater than 180 degrees, causing some vertices to point inward.
- Polygons are classified based on the number of sides, with a dodecagon having twelve sides and a general "n-gon" representing any polygon with 'n' sides.
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Description
Prepare for your Geometry Chapter 1 test with these flashcards covering essential vocabulary. Each term includes a definition to help reinforce your understanding of basic geometric concepts. Study terms like defined terms, undefined terms, lines, and planes.
