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Loci and constructions – WJECConstructing quadrilaterals

To draw constructions you need a pencil, ruler and a pair of compasses. Loci are used to identify areas that satisfy criteria such as a given distance from a point or halfway between two lines.

Part of MathsGeometry and Measure

Constructing quadrilaterals

When constructing quadrilaterals, we usually form them from two triangles. In order to construct our triangles, we need to know either:

  • the length of three sides (SSS)
  • one side and two angles (ASA) or
  • two sides and an angle (SAS)

When constructing quadrilaterals, you need at least five pieces of information. The information you are provided with, can be either side lengths (S), angles (A) or the length of the diagonals (D).

Using the information you have, look to see which triangles you can construct. You only have to accurately construct three sides of the quadrilateral, as you can complete the shape by connecting the corners of the remaining sides.

Example one

An infographic showing how a quadrilateral can be constructed from two triangles. The lengths of all sides are known and are labelled.

Example two

An infographic showing how a quadrilateral can be constructed from two triangles. The lengths of some sides and size of some angles are known and are labelled.
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