7th Class Mathematics Practical Geometry

PRACTICAL GEOMETRY

FUNDAMENTALS

•           A ruler protractor and compass are used for constructions.
•           Given a line 1 and a point P not on it, a line parallel to 1 can be drawn through the point P, using the idea of 'equal alternate angles' or 'equal corresponding angles'.
•           Students should draw rough sketch before actually constructing the triangle. This is very important for students to get the feel of the triangle.
•           Three independent measurements are required to construct a triangle.
•           The sum of lengths of any two sides of a triangle is greater than its third side»
•           The difference of lengths of any two sides of a triangle is lesser than its third side.
•           The sum of angles in a triangle is\[180{}^\circ \].
•           The exterior angle of a triangle is equal in measure (i.e. is equal to the sum) of interior opposite angles.
•           The following cases of congruence of triangles, help us construct the triangle.

(a) S.S.S: A triangle can be drawn given the lengths of its three sides.

(b) S.A.S: A triangle can be drawn given the lengths of any two sides and the measure of the angle between them.

(c) A.S.A: A triangle can be drawn given the measures of two angles and the length of the side included between them.

(d) R.H.S: A right angled triangle can be drawn given the length of hypotenuse and the length of one of its legs.