Geometry Chapter 1 Test Flashcards

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.