Constructing figures from measurements

Use a ruler for lengths and straight lines, a protractor for measured angles, compasses for equal distances, and a set square for perpendicular or parallel lines. For a three-side triangle construction, the intersecting arcs locate a point at both required distances.

Example

To construct \(\triangle ABC\) with \(AB=6\text{ cm}\), \(AC=5\text{ cm}\), \(BC=4\text{ cm}\): draw \(AB\); draw an arc of radius 5 cm centred at \(A\), and one of radius 4 cm centred at \(B\); label their intersection \(C\) and join \(AC\) and \(BC\). Retain the arcs.

The arcs encode \(AC=5\) and \(BC=4\). A reflected intersection below AB gives a congruent triangle; choose the requested side. When angles are supplied, measure them with a protractor and mark the stated lengths.

Check feasibility before drawing: the longest side of a triangle must be shorter than the sum of the other two. Use the stated data to build quadrilaterals as connected triangles or with the required parallel/perpendicular sides. Never measure a sketch labelled “not drawn to scale”.