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In this section, we revisit key geometric concepts such as line segments, rays, and various types of angles including acute, obtuse, and complementary angles. Definitions of collinear points, adjacent angles, linear pairs, and vertically opposite angles are also explored, laying a foundation for understanding the properties of lines and angles.
In this section, we focus on fundamental geometric terms that serve as the building blocks in the study of lines and angles. We start by defining:
We also introduce key concepts such as collinear points, which refer to three or more points lying on the same line, while non-collinear points do not. The section covers the definition of an angle formed when two rays meet at a vertex. Different types of angles are classified as follows: - Acute Angle: 0° < angle < 90° - Right Angle: angle = 90° - Obtuse Angle: 90° < angle < 180° - Straight Angle: angle = 180° - Reflex Angle: 180° < angle < 360°
Additionally, we explore the relationships between angles, defining complementary angles (sum equals 90°) and supplementary angles (sum equals 180°). Concepts such as adjacent angles (sharing a common vertex and arm) and linear pairs (two adjacent angles summing to 180°) are defined, alongside vertically opposite angles, which occur at the intersection of two lines. Understanding these basic terms and definitions is crucial for grasping more complex geometric principles in upcoming chapters.
Line Segment: A finite part of a line with two endpoints.
Ray: A part of a line with one endpoint extending infinitely in one direction.
Collinear Points: Points that lie on the same line.
Adjacent Angles: Angles that share a common vertex and arm.
Complementary Angles: Two angles that add up to 90 degrees.
Acute angles are sharp like a knife, less than 90 is their life!
Imagine two friends, Ray and Segment, meeting at a point, they decide how far they'll go: Segment to a stop, and Ray forever onward!
Use 'CAS' for angles: C = Complementary, A = Acute, S = Supplementary to remember their types!
A line segment connecting points A(2, 3) and B(5, 6) has endpoints A and B.
Complementary angles could be a 30° angle and a 60° angle, totaling 90°.
Term: Line Segment
Definition: A part of a line with two endpoints.
A part of a line with two endpoints.
Term: Ray
Definition: A part of a line that extends infinitely in one direction.
A part of a line that extends infinitely in one direction.
Term: Line
Definition: A straight one-dimensional figure that extends indefinitely in both directions.
A straight one-dimensional figure that extends indefinitely in both directions.
Term: Collinear Points
Definition: Three or more points that lie on the same straight line.
Three or more points that lie on the same straight line.
Term: NonCollinear Points
Definition: Points that do not lie on the same straight line.
Points that do not lie on the same straight line.
Term: Adjacent Angles
Definition: Angles that have a common vertex and a common arm.
Angles that have a common vertex and a common arm.
Term: Linear Pair
Definition: A pair of adjacent angles whose non-common arms form a straight line.
A pair of adjacent angles whose non-common arms form a straight line.
Term: Vertically Opposite Angles
Definition: The angles opposite each other when two lines intersect.
The angles opposite each other when two lines intersect.
Term: Acute Angle
Definition: An angle measuring less than 90 degrees.
An angle measuring less than 90 degrees.
Term: Obtuse Angle
Definition: An angle measuring greater than 90 degrees but less than 180 degrees.
An angle measuring greater than 90 degrees but less than 180 degrees.
Term: Complementary Angles
Definition: Two angles whose measures add up to 90 degrees.
Two angles whose measures add up to 90 degrees.
Term: Supplementary Angles
Definition: Two angles whose measures add up to 180 degrees.
Two angles whose measures add up to 180 degrees.