Plane Geometry: Lines, Angles and Polygons — CSEC Technical Drawing
Plane geometry deals with flat (2D) shapes. This topic covers lines, angles and polygons and how to construct them accurately.
Angles
- Acute — less than 90°.
- Right — exactly 90°.
- Obtuse — between 90° and 180°.
- Reflex — greater than 180° (and less than 360°).
The angles in any triangle add up to 180°; the angles in a quadrilateral add up to 360°.
Types of line
- Parallel lines stay the same distance apart and never meet.
- Perpendicular lines meet at 90°.
- To bisect a line or angle means to divide it into two equal parts.
Triangles
- Equilateral — three equal sides and three 60° angles.
- Isosceles — two equal sides and two equal angles.
- Scalene — all sides and angles different.
- Right-angled — one 90° angle.
Polygons
A polygon is a closed shape with straight sides:
| Sides | Name |
|---|---|
| 3 | triangle |
| 4 | quadrilateral |
| 5 | pentagon |
| 6 | hexagon |
| 8 | octagon |
A regular polygon has all sides and angles equal. Each interior angle of a regular polygon = (n − 2) × 180 ÷ n. For a hexagon this is 120°.
Constructions
You should be able to bisect lines and angles, construct perpendiculars, and construct regular polygons (e.g. a hexagon in a circle) using only a compass and straight edge.
Exam tips
- Learn the four angle types by their size ranges.
- Triangle angles sum to 180°; quadrilateral to 360°.
- Know the polygon names by number of sides.
- Bisect = divide into two equal parts; perpendicular lines meet at 90°.