Chap 4 Practical Geometry

Chap 4

Practical Geometry

SOME IMPORTANT FACTS

1.      To construct a quadrilateral uniquely, it is necessary to have the knowledge of at least five of its parts. To construct a quadrilateral data about five parts of a quadrilateral are sufficient in following cases.

i)                     Four sides and one diagonal .

ii)                  Three side and two diagonal .

iii)                Four sides and one angle .

iv)                Three sides and two included angles.

v)                  Three angles and their two included sides.

2.      Data about five parts of a quadrilateral in order to be sufficient must also satisfy ;

i)                    The triangle inequality and

ii)                  Angle sum property of a triangle, ( sum of three interior angles of triangle is 180⁰

Wherever applicable.

3.      It is possible to construct a quadrilateral with other sufficient data ( other than the five simple cases ) , where less than five parts but some other relations between the parts are given.

4.      In all cases , it is convenient and helpful to draw rough sketch of the quadrilateral and indicate the data on it.