Parallel Lines Definition
The definition for parallel lines states that if the lines lie in the same plane and if they don’t touch or meet the other lines at any point of the line, then these lines are termed to be parallel lines. If there are two parallel-lines PQ and RS, then it is said that the line PQ is parallel to the line RS.
When are two lines said to be parallel?
Two given lines are said to be parallel-lines if it satisfies any one of the following conditions:
• If they have a pair of alternate interior angles which are of equal measure.
• If they have a pair of corresponding angles which are of equal measure.
• If any one pair of interior angles which lie on the same side of the transversal are supplementary angles.
Constructing Parallel Lines
Now let us see how to construct parallel-lines. Draw a line AB and mark a point C at some place above the line AB. Through C, draw a transverse line which cuts AB at D. The transverse line crosses C as well as AB. The line can cut the straight line at any angle. With D as centre and with more than half of CD as radius draw an arc which cuts CD at E and AB at F. With C as centre and with the same radius, draw a similar arc on the transverse line above the point C to cut the transverse line at G.
Now change the radius. The width of the lower arc that crosses the two lines AB and CD is taken as the compass width i.e. the radius. With G as centre draw an arc on the upper arc to cut at H. Now a straight line is drawn through C and H. We can see that the straight line CH is parallel to line AB.
Thus two parallel-lines AB and CH are constructed.
Properties of Parallel Lines
Consider there are two parallel-lines A and B which are cut by a transversal line. At the point of intersection of the transversal line with the two parallel-lines, the following properties will be met:
• The pair of acute angles formed in the parallel-lines is equal.
• The pair of obtuse angles formed in the parallel-lines is equal.
• The acute angles formed are supplementary to the obtuse angles formed.
• Equally measuring alternate interior angles are present.
• Equally measuring corresponding angles are present.
• The sum of the two interior angles which are present on the same side of the transversal is equal to 180 degrees.
• The sum of any acute angle with any obtuse angle is equal to 180 degrees.
