Unit 1 Geometry Basics Flashcards

Basic Geometry Concepts

• Point: Represents a specific location without size or shape, fundamental in geometry.
• Line: Composed of infinitely many points, extends without thickness or width.
• Line Segment: A part of a line defined by two distinct endpoints, measurable in length.
• Ray: A portion of a line that starts at a point and extends infinitely in one direction.
• Plane: A flat, two-dimensional surface stretched infinitely in all directions, formed by points.

Relationships and Properties

• Collinear: Describes points that reside on the same straight line.
• Coplanar: Refers to points that lie within the same flat surface (plane).
• Congruent Segments: Segments that have identical length, implying equality in measurement.

Important Postulates and Theorems

• Segment Addition Postulate: States that if point B is between points A and C on a line, then the sum of the lengths of segments AB and BC equals the length of segment AC.
• Distance Formula: Utilized to calculate the distance between two points on a coordinate plane.
• Midpoint Formula: Determines the midpoint between two endpoints, effectively finding their average position.

Bisectors and Intersections

• Segment Bisector: A line, segment, or plane that divides another segment into two equal parts at the midpoint.
• Perpendicular: Two lines intersecting to form a right angle (90 degrees).
• Perpendicular Bisector: A bisector that intersects a segment at its midpoint and forms right angles with it.

Angles and Their Types

• Angle: Formed by two rays sharing a common endpoint called the vertex.
• Vertex: The point where two rays or lines meet to form an angle.
• Right Angle: Measures exactly 90 degrees, creating a quarter turn.
• Acute Angle: Measures less than 90 degrees, appearing sharp in appearance.
• Obtuse Angle: Measures more than 90 degrees, creating a wider opening.

Angle Relationships

• Straight Angle: A flat angle measuring 180 degrees, resembling a straight line.
• Congruent Angles: Angles that have identical measures, indicated by specific symbols.
• Adjacent Angles: Share a side and vertex, positioned next to each other without overlap.
• Angle Addition Postulate: States that the sum of two adjacent angles equals the measure of the larger angle formed.
• Angle Bisector: Divides an angle into two equal parts, creating two congruent angles.

Special Angle Relationships

• Vertical Angles: Pair of angles opposite each other at the intersection of two lines; always congruent.
• Complementary Angles: Two angles whose measures add up to 90 degrees.
• Supplementary Angles: Two angles that sum to 180 degrees, forming a linear pair.
• Linear Pair: Comprises two adjacent angles that are supplementary, lying on a straight line.