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Geometry
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India
Class IX

Identifying Parallel Lines

Lesson
Practice
Lesson

We've already looked at some angle relationships on parallel lines. Just to recap:

  • Corresponding angles on parallel lines are equal.
  • Alternate angles on parallel lines are equal.
  • Co-interior angles inside parallel lines are equal.

We have mainly used these rules to find the values of angles. However, we can also use these angle relationships to prove whether or not lines are parallel. To do this , we use the rules in reverse.

We can say:

  • If two corresponding angles are equal, then the two lines that the transversal cross are parallel.
  • If two alternate angles are equal, then the two lines that the transversal cross are parallel.

  • If two co-interior angles add up to $180^\circ$180°, then the two lines that the transversal cross are parallel.

 

Let's look through some examples and see if you can determine whether or not the lines are parallel.

 

Examples

Question 1

Are the lines $AB$AB and $CD$CD parallel?

 

Question 2

$AB$AB and $CD$CD are not parallel because:

 

 

Outcomes

9.G.LA.1

If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and the converse. If two lines intersect, the vertically opposite angles are equal. Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines.

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