Overview
This lecture introduces the concepts of lines, angles, polygons, diagonals, and classifications of polygons, focusing on their basic properties and differences.
Lines and Rays
- A curved line is formed by moving a point freely in any direction.
- A straight line is formed by moving a point without changing its direction.
- A line segment has two endpoints.
- A ray has one endpoint and extends infinitely in one direction.
Angles
- An angle is formed when two rays emerge from a common point, called the vertex.
- The size of an angle can be visualized by rotating one ray about the vertex.
Polygons and Their Classification
- A polygon is named based on its number of sides or vertices.
- Triangle: 3 sides/vertices.
- Quadrilateral: 4 sides/vertices.
- Pentagon: 5 sides/vertices.
- Hexagon: 6 sides/vertices.
- Heptagon: 7 sides/vertices.
- Octagon: 8 sides/vertices.
Diagonals of Polygons
- A diagonal is a line segment connecting two non-consecutive vertices of a polygon.
- In a quadrilateral, there are two diagonals; in a pentagon, there are more.
Convex and Concave Polygons
- A convex polygon has all diagonals inside the figure (none in the exterior).
- A concave polygon has some diagonals or parts of them lying outside the figure.
- The focus will be on convex polygons in this course.
Regular and Irregular Polygons
- A regular polygon is both equiangular (equal angles) and equilateral (equal sides).
- An irregular polygon lacks equal sides or equal angles.
- Examples: Square and equilateral triangle are regular; rectangle and right triangle are irregular.
Key Terms & Definitions
- Curved Line — Path traced by a point moving freely in any direction.
- Line Segment — Part of a line bounded by two endpoints.
- Ray — Part of a line with one endpoint, extending infinitely in one direction.
- Angle — Formed by two rays with a common endpoint (vertex).
- Polygon — Closed figure with straight sides.
- Diagonal — Line segment joining non-consecutive vertices of a polygon.
- Convex Polygon — All diagonals lie within the polygon.
- Concave Polygon — At least one diagonal lies outside the polygon.
- Regular Polygon — Polygon with all sides and angles equal.
- Irregular Polygon — Polygon with unequal sides or angles.
Action Items / Next Steps
- Review types of quadrilaterals and their properties for the next class.