 # Practical Geometry

## Construction of a line parallel to a given line through a point that does not lie on the line can be done by using a ruler and a pair of compasses only. Any one of the following two properties is used to verify that the lines drawn are parallel: When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel. When a transversal cuts two lines, such that pairs of alternate interior angles are equal, then the lines have to be parallel. A triangle is a simple closed plane figure made up of three line segments. A triangle has three vertices, three sides and three angles. Some of the properties of a triangle are: Exterior angle property: The exterior angle of a triangle is equal to the sum of two opposite interior angles. Angle sum property: Sum of all interior angles of a triangle is 180°. The sum of the lengths of any two sides of a triangle is greater than the third side. In any right-angled triangle, the square of the length of hypotenuse is equal to the sum of the squares of the lengths of the other two sides. i.e.,Hypotenuse2 = Base2 + Altitude2 A triangle can be constructed in the following four cases: SSS criterion: When lengths of three sides are given. SAS criterion: When lengths of two sides and the included angle are given. ASA criterion: When two angles and the included side are given. RHS criterion: When the length of one side and hypotenuse of a right-angled triangle are given.

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