1. Angles and Triangles Cian Taylor Email: cian.taylor@ireland.comcian.taylor@ireland.com Web: http://eduspaces.net/ciantaylorhttp://eduspaces.net/ciantaylor

2. About me I am an Irish secondary school teacher of Maths and Science. Check out my eduspace page at http://eduspaces.net/ciantaylor http://eduspaces.net/ciantaylor Feel free to use this presentation for educational purposes but please leave the title slide with my contact details intact.

3. Equilateral Triangle Equilateral Triangle: The 3 sides are of equal length

4. Equilateral Triangle The 3 corner angles are 60 degrees.

5. Isosceles Triangle Two of the sides are of equal length. The third side is a different length

6. Isosceles Triangle Two of the corner angles are equal. The third angle is different.

7. Some more Isosceles Triangles... These two sides are equal. The angles where the equal sides meet the third side are equal. The third angle is different in size.

8. Some more Isosceles Triangles... Equal Sides Equal Angles

9. Some more Isosceles Triangles... Equal Sides Which two angles are equal?

10. Some more Isosceles Triangles... Which two angles are equal?

11. Scalene Triangle All angles are different sizes. All sides are different lengths.

12. Right-angled Triangle In a right-angled triangle, one of the corner angles is a 90 degree angle. 90 degree angle.

13. More Right-angled Triangles In a right-angled triangle, one of The corner angles is a 90 degree angle. 90 degree angle.

14. Angles in a Triangle The angles of a triangle, added together, form a straight angle, 180⁰.

15. This condition holds for any Triangle (Right-angled).

16. This condition holds for any Triangle (Equilateral).

17. Angles in a Triangle (Isosceles)

18. This condition holds for any Triangle (Scalene).

19. Using this rule A B C

20. Sample problem: work out the value of the angle x in the triangle shown. What type of triangle is this?

21. Sample problem 2: work out the values of the angles x and y in the triangle shown. What type of triangle is this?

22. Opposite Angles When two lines intersect, 4 angles are formed. Angles which are opposite each other, are equal. The two angles in red are opposite angles, they are equal in size. The two angles in yellow are opposite angles, they are equal in size.

23. Angles and parallel lines. When a line crosses 2 parallel lines many of the angles formed are equal. The angles in red are all equal in size. The angles in yellow are all equal in size.

24. Angles and parallel lines. All the acute angles are equal and all the obtuse angles are equal. Some of these angles have special names.

25. Corresponding Angles

26. Corresponding Angles are equal.

27. You can spot corresponding angles by looking for the following shapes

29. Corresponding Angles: ‘F’ shape

30. Alternate angles

31. Alternate angles are equal

32. You can spot alternate angles by looking for the following shapes

33. Alternate Angles: ‘Z’ shape

34. Interior Angles Interior Angles add to 180⁰

35. Angles and parallel lines. Interior Angles Interior Angles add to 180⁰

36. You can spot interior angles by looking for the following shapes

37. Interior Angles: ‘C’ shape

38. Work out the value of the angles x and y in the diagram below. Using the opposite angle rule, y and 60 are equal Using the alternate angle rule, y and x are equal

39. Work out the value of the angles x and y in the diagram below. Using the corresponding angle rule, y and 125 are equal Using the straight angle rule,

40. Work out the value of the angles x and y in the diagram below. Using the interior angle rule, the angles shown add to 180⁰. So the angle in red is 55⁰. Using the opposite angle rule, Using the corresponding angle rule,

41. Work out the value of the angle p in the diagram below. The angles shown are corresponding angles. Using the opposite angle rule,

42. Sample problem: the line L is parallel to side rs of the triangle, work out the angles x and y. Step1: As rs and L are parallel, we can use the alternate angle rule: Step2: Triangle rule: