Lines, Planes, Theorems: Exploring Geometric Concepts
In this section, you'll delve into the properties of lines and planes in geometry. Understand the definitions of parallel, intersecting, and skew lines, as well as parallel planes. Explore the theorems of transitivity of parallel lines and properties of perpendicular lines. Visual aids accompany the explanations to enhance your comprehension of these fundamental geometric concepts.
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Presentation Transcript
Section 3.1 Exploring Lines and Planes
Parallel Lines Are coplanar lines that do not intersect. Parallel Lines have the same slope. Intersecting Lines- are coplanar and have exactly one point in common. If they meet at right angles, they are perpendicularotherwise they are oblique
Theorem 3.1 Transitivity of Parallel Lines- if two lines are parallel to the same line, then they are parallel to each other.
Theorem 3.2 Property of Perpendicular Lines- if two coplanar lines are perpendicular to the same line, then they are parallel to each other. Remember that perpendicular lines have slopes that are negative reciprocals
Skew Lines Are two lines that do not lie in same plane. They do not intersect and are not parallel B C D A G F E
Planes Parallel planes are two planes that do not intersect. EX: floor and ceiling of most rooms are parallel. Sketch: 1. Two planes that intersect but are not perpendicular. 2. Two parallel planes, each perpendicular to a third plane.
