Choose the instrument from the task
| Task | Method |
|---|---|
| Measured angle in a scale drawing | Use a ruler and protractor; measure the stated angle from the correct ray. |
| Triangle from three side lengths | Draw one side; intersect arcs from its endpoints using compasses; join the third vertex. |
| Perpendicular bisector | With the same compass radius greater than half the segment, draw intersecting arcs above and below from both endpoints. Join the intersections. |
Retain construction arcs. A perpendicular bisector meets a segment at \(90^\circ\) and divides it into equal lengths. Two mirror-image positions of a triangle's third vertex give congruent triangles; use the side of the base requested.
Constructing an angle bisector
From the vertex \(A\), draw one arc cutting the two arms at \(D\) and \(E\). Without changing the compass radius between the two centres, draw arcs from \(D\) and \(E\) that meet inside the angle at \(P\), distinct from \(A\). Draw the ray \(AP\). Keep all three construction arcs visible.
The construction gives \(AD=AE\) and \(DP=EP\); \(AP\) is common. Hence \(\triangle ADP\equiv\triangle AEP\) (SSS), so \(\angle DAP=\angle PAE\) (corresponding angles). This proves that the ray bisects the angle without assuming the halves are equal.
Lengths and scales
A scale \(1:n\) compares drawing length with actual length in the same unit. Multiply by \(n\) to recover an actual length. Since \(1\text{ km}=100\,000\text{ cm}\), convert centimetres to kilometres only after applying the scale.
A measurement is approximate. Draw at the requested actual scale, read the instrument carefully and state the unit. Do not measure an illustration labelled “not drawn to scale”.
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