Notes for Practical Geometry

A triangle has six elements – 3 sides and 3 angles. To construct a unique triangle, 3 elements out of six elements are required under a certain combination. A quadrilateral has 8 elements – 4 sides and 4 angles. In addition to these elements a quadrilateral has 2 diagonals which play an important role in determining the size and shape of a quadrilateral. Thus a quadrilateral has 10 elements (4 sides, 4 angles and 2 diagonals) or measurements.

To construct a unique quadrilateral we need to know 5 measurements (elements).

With the help of the following measurement we can construct quadrilaterals.

(i) Four sides and a diagonal.

(ii) Three sides and two diagonals.

(iii) Four sides and an angle.

(iv) Three sides and two included angles.

(v) Two adjacent sides and three angles.

(vi) Using special properties of a square or a rhombus, etc.