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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