7th Class Mathematics Practical Geometry Practical Geometry

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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Notes - Practical Geometry
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