What are Intersecting and Non-Intersecting Lines?
- Intersecting lines are lines that cross each other at exactly one point (called the point of intersection)
- Non-intersecting lines (parallel lines) are lines that never meet, no matter how far they are extended
What are Different Angle Pairs?
When two lines intersect or when lines are combined, various angle pairs are formed:
| Angle Pair | Definition | Diagram Description | Property |
|---|---|---|---|
| **Supplementary Angles** | Two angles whose sum is 180° | 110° + 70° = 180° | Each is supplement of the other |
| **Adjacent Angles** | Two angles sharing a common vertex and common arm, with non-common arms on opposite sides | Angles next to each other | They do not overlap |
| **Linear Pair** | Adjacent angles formed when two lines intersect; their non-common arms are opposite rays | ∠AOC and ∠COB sharing ray OC | Sum = 180° |
| **Vertically Opposite Angles** | Angles opposite each other when two lines intersect | ∠AOC and ∠BOD | They are always EQUAL |
Real-Life Examples:
- Intersecting lines: Crossroads, scissors, window grills
- Parallel lines: Railway tracks, opposite edges of a notebook
- Complementary angles: Acute angles in a right triangle, clock hands at 3:00 (90°)
- Linear pair: Door opening, book pages