Questions and Answers
What is a point?
What are points that lie on the same line called?
Collinear
What do we call points that do not lie on the same line?
Non collinear
Define a plane.
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What is the term for points that lie on the same plane?
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Define a postulate.
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What is an angle?
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What do we call the common endpoint of two rays?
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What is the measure of a right angle?
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Define obtuse angle.
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What is a straight angle?
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What do we call part of a line consisting of two endpoints?
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Define parallel lines.
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What is the definition of complementary angles?
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What are vertical angles?
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Define adjacent angles.
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What do we call angles that form a linear pair?
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Study Notes
Basic Geometric Concepts
- Point: Represents a location with no size or dimension; denoted by a single capital letter.
- Line: Composed of infinitely many points extending endlessly in both directions; identified by two points on the line and a lowercase letter.
- Collinear Points: Points that lie on the same straight line.
- Non-Collinear Points: Points that do not align on the same straight line.
- Plane: A flat, two-dimensional surface with no thickness, identified by a capital letter or three non-collinear points.
Relationships Between Points and Lines
- Coplanar: Points and lines that reside within the same plane.
- Non-Coplanar: Points and lines that do not share the same plane.
- Postulate: A basic accepted statement that requires no proof.
Angles and Their Properties
- Angle: Formed by two rays sharing a common endpoint (vertex).
- Vertex: The shared endpoint of two rays that create an angle.
- Sides: The two rays that compose an angle.
- Degree: The standard unit used to measure angles.
Types of Angles
- Acute Angle: Measures greater than 0 degrees but less than 90 degrees.
- Right Angle: Measures exactly 90 degrees, often denoted by a box in the angle's corner.
- Obtuse Angle: Measures greater than 90 degrees but less than 180 degrees.
- Straight Angle: Measures exactly 180 degrees, appearing as a straight line.
Line Segments and Rays
- Segment: A part of a line defined by two endpoints and all points in between.
- Ray: A line extending indefinitely in one direction, beginning at a single endpoint.
- Opposite Rays: Two rays sharing an endpoint and extending in opposite directions, forming a straight line.
Lines and Planes
- Parallel Lines: Coplanar lines that do not intersect.
- Skew Lines: Lines on different planes that are neither parallel nor intersecting.
- Parallel Planes: Two planes that do not intersect each other.
Segment and Angle Relationships
- Congruent Segments: Segments that are identical in length.
- Midpoint: A point that precisely divides a segment into two equal parts.
- Segment Bisector: A line or segment that intersects another segment at its midpoint.
Perpendicular Relationships
- Perpendicular Lines: Lines that intersect to create a right angle (90 degrees).
- Perpendicular Bisector: A line perpendicular to a segment at its midpoint.
- Angle Bisector: A ray that divides an angle into two equal angles.
Complementary and Supplementary Angles
- Supplementary Angles: Two angles whose sum equals 180 degrees.
- Vertical Angles: Angles opposite each other formed by intersecting lines, always equal in measure.
- Adjacent Angles: Angles that share a common side and vertex.
- Linear Pair: Adjacent angles that combine to form a straight line (180 degrees).
- Complementary Angles: Two angles whose sum equals 90 degrees.
Studying That Suits You
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Description
Test your understanding of the fundamentals of geometry with these flashcards from Unit 1. Each card features essential definitions like 'Point,' 'Line,' and 'Collinear' to help you grasp basic concepts crucial for your geometric studies.
