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Parallel Lines

Non-intersecting straight lines, which do not meet when produced however far on either side, are called ‘parallel’.

parallel lines

The distance between the parallel lines AB and CD is the length of the perpendicular PQ from P (any point in AB) to CD.

parallel lines

The distance between any two parallel lines will always remain the same. A line is parallel to itself. Through a given point, only one straight line can be drawn parallel to another straight line.

A ‘transversal’ is a straight line which cuts two or more straight lines.

parallel lines

The pair of angles 1 and 5, 2 and 6, 3 and 7, 4 and 8 are called ‘corresponding angles’.

The pair of angles 3 and 5, 4 and 6 are called ‘alternate angles’.

Example: Find the value of x.

parallel lines

10x + 5 = 65° (corresponding angles)

10x + 5 – 5 = 65° – 5

10x = 60°

\frac{10x}{{10}} = \frac{60}{{10}} => x = 6

CHECK POINT

 

  1.   What is the measure of the indicated angle?
parallel lines

2. Solve for x:

parallel lines

                                                                                                                                                                                                                                              

  1. True or False:                                                                                                                                                                                                                             When a transversal cuts two parallel lines, then the pairs of corresponding angles so formed are equal. __________
  2. Solve for x:                                                                                                          parallel7-300x274
  3. Find the value of x:                                                                                                                                                  parallel8-300x224
Answer key
  1. 78°
  2. 9
  3. True
  4. 6
  5. 8

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