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Practical Geometry

Category : 7th Class

Practical Geometry

A ruler and compasses are used for constructions.
Given a line \[l\] and a point not on it, a line parallel to \[l\] can be drawn using the idea of 'equal alternate angles' or 'equal corresponding angles'.
Three independent measurements are required to construct a triangle.
A rough sketch is drawn with the given measurements before actually constructing the 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\[{{180}^{o}}\].
The exterior angle of a triangle is equal in measure to the sum of interior opposite angles.

The following cases of congruence of triangles are used to construct a triangle.

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

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

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

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

(a) an equilateral triangle, if all of its sides are equal.(b) an isosceles triangle, if any two of its sides are equal.

(c) a scalene triangle, if all of its sides are of different lengths.

(a) an acute angled triangle, if each one of its angles measures less than \[{{90}^{o}}\].

(b) a right angled triangle, if any one of its angles measures\[{{90}^{o}}\].

(c) an obtuse angled triangle, if any one of its angles measures more than 90°.

Pythagoras' theorem: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the remaining two sides.

\[\operatorname{Here},A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\]