Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal (ACMMG163)
Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (ACMMG164)
Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (ACMMG164)
PARALLEL LINES
Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. Just remember:
Always the same distance apart and never touching.The red line is parallel to the blue line in both these cases:
Parallel lines also point in the same direction.
Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. Just remember:
Always the same distance apart and never touching.The red line is parallel to the blue line in both these cases:
Parallel lines also point in the same direction.
PAIRS OF ANGLES
When parallel lines get crossed by another line (which is called aTransversal), you can see that many angles are the same, as in this example:
These angles can be made into pairs of angles which have special names
When parallel lines get crossed by another line (which is called aTransversal), you can see that many angles are the same, as in this example:
These angles can be made into pairs of angles which have special names
The pairs of angles on opposite sides of the transversal but inside the two lines are called
Alternate Interior Angles.
In this example, these are Alternate Interior Angles:
Alternate Interior Angles.
In this example, these are Alternate Interior Angles:
- c and f are Alternate Interior Angles
- d and e are also Alternate Interior Angles
The pairs of angles on opposite sides of the transversal but outside the two lines are called
Alternate Exterior Angles.
In the example:
Alternate Exterior Angles.
In the example:
- a and h are Alternate Exterior Angles
- b and g are also Alternate Exterior Angles
The pairs of angles on one side of the transversal but inside the two lines are called Consecutive Interior Angles (or Co-Interior Angles).
In this example, these are Consecutive Interior Angles:
In this example, these are Consecutive Interior Angles:
- d and f are Consecutive Interior Angles
- c and e are also Consecutive Interior Angles
TESTING FOR PARALLEL LINES
Some of those special pairs of angles can be used to test if lines are really parallel.
Some of those special pairs of angles can be used to test if lines are really parallel.
If any pair of of... Example
Corresponding angles are equal, or, a=e
Alternate interior angles are equal, or, c=f
Alternate exterior angles are equal, or, b=g
Consecutive interior angles add up to 180 degrees d+f = 180 degrees
Then the lines are parallel.
Corresponding angles are equal, or, a=e
Alternate interior angles are equal, or, c=f
Alternate exterior angles are equal, or, b=g
Consecutive interior angles add up to 180 degrees d+f = 180 degrees
Then the lines are parallel.
You can complete a set of 10 questions on http://www.mathsisfun.com/geometry/parallel-lines.html
Use the worksheet below to practise identifying the different angle pairs.
angles-in-parallel-lines-colouring-fun.pdf | |
File Size: | 324 kb |
File Type: |