6.1 Introduction
- Geometry studies shapes, sizes, positions, and properties of figures.
- Lines and angles are the basic building blocks of geometry.
- Understanding these helps in triangles, polygons, and parallel lines.
6.2 Basic Terms and Definitions
| Term | Definition |
|---|---|
| Point | Location in space with no length, breadth, or thickness |
| Line | Straight connection between points extending in both directions |
| Line segment | Part of a line between two points |
| Ray | Part of a line with one fixed endpoint extending infinitely in one direction |
| Angle | Figure formed by two rays with common endpoint |
| Vertex | Common endpoint of an angle |
| Complementary angles | Two angles whose sum = 90° |
| Supplementary angles | Two angles whose sum = 180° |
6.3 Intersecting and Non-Intersecting Lines
- Intersecting lines: Lines that meet at a point.
- Non-intersecting lines: Lines that do not meet.
- Parallel lines are non-intersecting lines in the same plane.
6.4 Pairs of Angles
- Adjacent angles: Share a common vertex and side
- Linear pair of angles: Sum = 180°
- Vertically opposite angles: Equal angles formed by intersecting lines
- Corresponding angles: Formed when a transversal intersects two lines; equal if lines are parallel
- Alternate interior angles: Equal if lines are parallel
- Alternate exterior angles: Equal if lines are parallel
- Co-interior (consecutive interior) angles: Sum = 180° if lines are parallel
6.5 Lines Parallel to the Same Line
- Theorem: If two lines are parallel to the same line, then they are parallel to each other.
- Symbol: If l || m and m || n, then l || n.
Quick Short Q&A (Most Possible)
| Question | Short Answer |
|---|---|
| What is a line segment? | Part of a line between two points |
| Ray definition? | Line with one endpoint, extends infinitely |
| Sum of complementary angles? | 90° |
| Sum of supplementary angles? | 180° |
| Vertically opposite angles? | Equal |
| Linear pair? | Sum = 180° |
| Alternate interior angles? | Equal if lines are parallel |
| Corresponding angles? | Equal if lines are parallel |
| Lines parallel to same line? | Parallel to each other |
| Intersecting lines? | Lines meeting at a point |