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 triangle is said to be,

** (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 triangle is said to be,

** (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.

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

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