Practical Geometry-Notes

Class VIII Math
Notes for Practical Geometry
WE KNOW THAT
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.
CONSTRUCTING A QUADRILATERAL
To construct a unique quadrilateral we need to know 5 measurements (elements).
Note: To construct a unique quadrilateral simply the knowledge of any five elements is not sufficient. We will need to know a combination of specific 5 elements.
VARIOUS COMBINATIONS OF ELEMENTS FOR CONSTRUCTING A UNIQUE QUADRILATERAL
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.