Measuring line segments, angles; reading maps and scale drawings
This topic combines practical skills (using a ruler and protractor) with map and scale interpretation.
Measuring with a ruler
- Always align the 0 mark with one endpoint, not the edge of the ruler.
- Read to the nearest mm unless otherwise specified.
- Hold ruler firmly to avoid slipping.
Measuring angles with a protractor
- Place protractor centre on the vertex.
- Align baseline with one ray.
- Read the angle on the inner or outer scale (whichever passes through 0° on your aligned ray).
- Common error: reading 130° as 50° (wrong scale).
Bearings
A bearing is a 3-figure direction: clockwise from north.
- N = 000° (or 360°).
- E = 090°.
- S = 180°.
- W = 270°.
Always state bearings as 3 digits: 045°, not 45°.
Maps and scale drawings
A scale describes the ratio between map distance and real distance, e.g. 1 : 25 000. (Topic G15 ↔ R2 overlap.)
Worked example: on a 1 : 50 000 map, the distance between two churches measures 7 cm. Real distance?
- 7 × 50 000 = 350 000 cm = 3.5 km.
Bearings problems
Worked example: from A, you walk 4 km on a bearing of 060°. State the position relative to A.
- 060° means 60° clockwise from north.
- Draw a line at 60° (clockwise from north arrow at A) and mark 4 km along it.
Three-figure bearing computation
To find a return bearing: add or subtract 180°. If the bearing from A to B is 120°, the bearing from B to A is 300°.
⚠Common mistakes
- Wrong protractor scale — pick the one matching your aligned 0°.
- Bearings without 3 digits — write 045°, not 45°.
- Measuring from end of ruler instead of the 0 mark.
- Reading clockwise from south instead of from north.
- Forgetting unit conversion in scale problems.
➜Try this— Quick check
A bearing of 075° from A. The reverse (B to A)?
- 075° + 180° = 255°.
AI-generated · claude-opus-4-7 · v3-deep-geometry