2. 1 Angles, Parallel Lines and Triangles BIRKDALE HIGH SCHOOL Mathematics Department Aim of the lesson:To use parallel lines, alternate angles and corresponding angles. Ma 3 Level 6

3. 2 The angle on a straight line is 180 o We have to start somewhere – this is our starting fact.

4. 3 Here are two straight lines + = and + = so = These are called vertically opposite angles also = Vertically opposite angles are equal 180 o

5. 4 Vertically opposite angles are equal

6. 5 a b c In the diagram below – find all the pairs of vertically opposite angles d e f g h i j k m n o q p Remember: look for scissor angles!!! 8 answers

7. 6 Here are two sets of vertically opposite angles Lets put them together

8. 7 Here are a pair of parallel lines … … and a transversal. Notice that lots of pairs of angles are equal Lets look at some ….

9. 8 These are called alternate angles …. … or Z angles Alternate angles are equal Here is another pair of alternate angles Here is a pair of angles that are equal For a dynamic demonstration http://www.rfbarrow.btinternet.co.uk /htmks3/Angle2.htmhttp://www.rfbarrow.btinternet.co.uk /htmks3/Angle2.htm - 1 st Rule

10. 9 a b c In the diagram below – find all the pairs of alternate angles d e f g h i j k m n o q p Remember: look for Z angles!!! 4 answers

11. 10 Here is a pair of angles that are equal These are called corresponding angles …. … or F angles Here is another pair of corresponding angles Corresponding angles are equal For a dynamic demonstration http://www.rfbarrow.btinternet.co.uk /htmks3/Angle2.htmhttp://www.rfbarrow.btinternet.co.uk /htmks3/Angle2.htm - 2 nd Rule

12. 11 a b c In the diagram below – find all the pairs of corresponding angles d e f g h i j k m n o q p Remember: look for F angles!!! 8 answers

13. 12 Here is a pair of angles that add up to 180º These are called allied angles …. … or C angles Here is another pair of allied angles Allied angles add up to 180º For a dynamic demonstration http://www.rfbarrow.btinternet.co.uk /htmks3/Angle2.htmhttp://www.rfbarrow.btinternet.co.uk /htmks3/Angle2.htm - 1 st Rule

14. 13 a b c In the diagram below – find all the pairs of allied angles d e f g h i j k m n o q p Remember: look for C angles!!! 4 answers

15. 14 Here are two different sets of parallel lines … and their transversals Lets put them together ….

16. 15 Find this straight line!!! Find this triangle!!! The angles on the straight line add up to 180 o … … so the angles of the triangle also add up to 180 o

17. 16 See a dynamic model of the previous page on: http://walter-fendt.de/m11e/anglesum.htm

18. 17 Vocabulary:Parallel Alternate Corresponding