Chapter 2: Lines and Angles
Look around your room and you will see geometry everywhere: the edge of your table is a line, the corner where two walls meet forms an angle, the tip of a pencil is almost a point. Geometry is the part of mathematics that studies shape, position, and the relations between them.
In this chapter we begin with the most fundamental objects of geometry. A point has no length, breadth, or height , it just marks a place. A line has length but no width, and goes on forever in both directions. A line segment is the part of a line between two points. A ray starts at a point and goes on forever in one direction. When two rays meet at a common starting point, they form an angle.
Once we know how to draw and name these objects, the natural next question is: how do we measure them? Line segments are measured with a ruler, in centimetres or millimetres. Angles are measured with a protractor, in degrees. We will learn both, and meet the special angles that show up so often that they have their own names , right angles, straight angles, acute angles, obtuse angles, and reflex angles.
What's inside
- Points, lines, line segments, and rays , the four foundational objects.
- Angles and their parts , vertex, arms, interior.
- Measuring angles with a protractor , using the half-circle of degrees.
- Types of angles , acute, right, obtuse, straight, reflex, complete.
- Special pairs of angles , complementary, supplementary, and the angles at a point.
Key results / Formula card
| Object | Description | Notation |
|---|---|---|
| Point | A precise location | , , |
| Line | Goes on forever both ways | |
| Line segment | Part of a line between two points | |
| Ray | Starts at a point, goes on forever | |
| Angle | Two rays sharing an endpoint |
| Type of angle | Measure |
|---|---|
| Acute | between and |
| Right | exactly |
| Obtuse | between and |
| Straight | exactly |
| Reflex | between and |
| Complete | exactly |
Two angles whose measures add to are complementary. Two angles whose measures add to are supplementary. All angles around a point sum to .
How to read this chapter
Keep a ruler, a sharp pencil, and a protractor next to you. Draw every figure that is described , geometry is learned with your hand, not just your eyes. Try every "Try it yourself" question and pay close attention to the Activity at the bottom of each subtopic.