1. Angles at Parallel Lines
Mathematics
Angles at Parallel Lines

2. Aims of the Lesson
To learn more key words and facts linked with angles formed when lines cross, especially when parallel lines are crossed.

3. Vertically Opposite Angles
When two lines cross, two pairs of vertically opposite angles are formed.
Angle Fact: Vertically opposite angles are equal
Equal
Equal
Equal
Equal

4. Angles at Parallel Lines
When a line (called a transversal) crosses a set of parallel lines, it forms four angles at each crossing point.
As the lines are parallel, they are travelling in the same direction, always the same distance apart from each other.
The transversal is one straight line so it cuts each of the parallel lines at the same angle.

5. Angles at Parallel Lines
As long as the transversal is not at 90° to the parallel lines (in which case all 8 angles will be equal), there will be…
4 acute angles (ALL equal in size) and
4 obtuse angles (ALL equal in size)
As each pairing of acute + obtuse angles form a straight line, they add up to 180°.

6. Corresponding Angles
Corresponding angles have the same position at each parallel lines.
Angle Fact:
Corresponding angles are equal.

7. Example of Corresponding Angles
Transversal
All the orange angles have the same position at each parallel line, i.e. above and to the left of the parallel lines

8. Alternate Angles
Alternate angles have vertically opposite positions at each parallel line.
Angle fact:
Alternate angles are equal.

9. Example of Alternate Angles
The orange angles are vertically opposite on different parallel lines, i.e. one is bottom left the other is top right
Transversal

10. Co-Interior or Supplementary Angles
(Co-)Interior angles (aka Supplementary Angles) are between the parallel lines on the same side of the transversal.
Angle fact:
Supplementary angles add up to 180°

11. Example of (Co-)Interior Angles
The orange and purple angles are between the parallel lines, both above the transversal. Together they add up to 180°
Transversal

12. What next?
Print out the notes called Angle5. Read through them and make sure you answer any questions.
Work through the MyMaths lesson and then its online HW called: Shape > Angles > Angles in Parallel Lines found at:
Save and complete the worksheets called:
AnglesPN-S1.xlsx and AnglesPara-S1.xlsx
Now move on to the Shape2 powerpoint