Worked examples
The question
Question: find out if the two lines are parallel.
The corresponding angles are 70° and 70°.
1 Name the angle pair
A line crosses two other lines.
It is called a transversal.
Our two angles are in the same place at each crossing: corresponding angles.
Together they make an F shape.
2 Use the parallel test
If the lines are parallel, both crossings look the same, so corresponding angles are equal.
And if they are equal, the lines are parallel.
70° and 70°: they are equal.
70 = 70
Careful!
For corresponding angles we ask: are they equal?
Careful: corresponding: equal, not adding to 180°
So the lines are parallel.
Answer: = parallel
We can draw the arrows on the lines now.
Let's look back.
First: name the angle pair.
Last: use the parallel test.
Answer Answer: = parallel
▶ Watch it solved
The question
Question: find out if the two lines are parallel.
The co-interior angles are 110° and 70°.
1 Name the angle pair
A line crosses two other lines.
It is called a transversal.
Our two angles are between the lines, on the same side of the transversal: co-interior angles.
Together they make a C shape.
2 Use the parallel test
Parallel lines make co-interior angles add up to 180°.
And if they add up to 180°, the lines are parallel.
So we add them: 110 + 70 = 180.
110 + 70 = 180
180 is 180.
They add up to 180°.
180 = 180
Careful!
For co-interior angles we do not ask: are they equal?
We ask: do they add up to 180°?
Careful: co-interior: add to 180°, not equal
So the lines are parallel.
Answer: = parallel
We can draw the arrows on the lines now.
Let's look back.
First: name the angle pair.
Last: use the parallel test.
Answer Answer: = parallel
▶ Watch it solved
The question
Question: find out if the two lines are parallel.
The alternate angles are 2x + 10 and 3x − 20, with x = 30.
1 Put x in
Put x = 30 in the angle 2x + 10.
2x + 10 = 2 × 30 + 10
That is 70°.
2x + 10 = 70
Put x = 30 in the angle 3x − 20.
3x − 20 = 3 × 30 − 20
That is 70°.
3x − 20 = 70
2 Name the angle pair
A line crosses two other lines.
It is called a transversal.
Our two angles are between the lines, on opposite sides of the transversal: alternate angles.
Together they make a Z shape.
3 Use the parallel test
Parallel lines make alternate angles equal.
And if they are equal, the lines are parallel.
70° and 70°: they are equal.
70 = 70
Careful!
For alternate angles we ask: are they equal?
Careful: alternate: equal, not adding to 180°
So the lines are parallel.
Answer: = parallel
We can draw the arrows on the lines now.
Let's look back.
First: put x in.
Then: name the angle pair.
Last: use the parallel test.
Answer Answer: = parallel
▶ Watch it solved
