1. Angle Properties and Parallel Lines Corresponding angles – sometimes known as F angles. ab c e d f gh c and h are corresponding angles and are equal. The F can be backwards… d and g are corresponding angles and are equal. The F can be upside down…. b and f are corresponding angles and are equal And finally the F can be upside down and backwards…. a and e are corresponding angles and are equal. Great Marlow School Mathematics Department

2. Which angle is corresponding to w? Which angle is corresponding to t? Angle Properties and Parallel Lines s t v w u x y z Which angle is corresponding to z? v x s y Which angle is corresponding to u? Corresponding angles – sometimes known as F angles. Great Marlow School Mathematics Department

3. b and g are alternate and are equal. c and e are alternate and are equal. Angle Properties and Parallel Lines ab c e d f gh Alternate angles – sometimes known as Z angles d and f are alternate and are equal. The Z can be backwards… The Z can be in two pieces. The Z can be in two pieces and backwards. a and h are alternate and are equal. Great Marlow School Mathematics Department

4. Which angle is alternate to s? s t v w u x y z Alternate angles – sometimes known as Z angles Angle Properties and Parallel Lines z Which angle is alternate to v? w Which angle is alternate to t? y Which angle is alternate to u? x Great Marlow School Mathematics Department

5. + d = 180 0 Adjacent angles - straight line. a = e Why? Corresponding angles are equal upside down and backwards F. Angle Properties and Parallel Lines Angles between parallel lines add up to 180 0 ab cd ef g h a + d = 180 0 Why? If we substitute e for a in the first statement we have….. a e Great Marlow School Mathematics Department

6. = h Prove that a = c using a different method. b f If we substitute f for b in the second statement we get… Angle Properties and Parallel Lines Vertically opposite angles are equal. ab cd ef g h b = f Why? Corresponding angles are equal upside down F b = h Why? Alternate angles are equal. Z in two pieces a + b = 180 adjacent angles - straight line b + c = 180 adjacent angles – straight line a + b = b + c both are equal to 180 - b = - b a = c...... Great Marlow School Mathematics Department

7. degrees reason x - 60 0 alternate angles y - 50 0 alternate angles z - 70 0 adjacent angles – straight line ((180 – (50+60)) degrees reason a - ____________________________ b - ____________________________ c - ____________________________ 35 0 50 0 60 0 x y z a b c 1. degrees reason a - 145 0 adjacent angles – straight line. (180 – 35) b - 35 0 vertically opposite angles c - 145 0 vertically opposite angles (a and c) Find the sizes of the angles marked with letters. You must give a reason for your answer. degrees reason x - ____________________________ y - ____________________________ z - ____________________________ 2. Great Marlow School Mathematics Department

8. Find the sizes of the angles marked with letters. You must give a reason for your answer. 55 0 d e f 3. 4. degrees reason d - 125 0 Angles between parallel lines add up to 180 0 e - 145 0 Angles at a point add up to 360 0 [360- (125+90)] f - 35 0 Angles between parallel lines add up to 180 0 degrees reason w - 50 0 Vertically opposite angles are equal. x – 50 0 Alternate angles are equal y - 40 0 Angles in a triangle add up to 180 0 [180-(50+90)] z - 40 0 Alternate angles are equal 50 0 x y z w degrees reason d - ____________________________ e - ____________________________ f - ____________________________ degrees reason w - ____________________________ x - ____________________________ y - ____________________________ z - _____________________________ Great Marlow School Mathematics Department

9. Find the sizes of the angles marked with letters. You must give a reason for your answer. 5. e 30 0 f g 50 0 75 0 degrees reason e - 20 0 50 0 is corresponding to e + 30 0 f - 20 0 alternate angles are equal g – 20 0 vertically opposite angles are equal 6. j k h degrees reason h - 75 0 Corresponding angles are equal j - 75 0 Isosceles triangle – angles opposite equal sides are equal k - 30 0 angles in a triangle add up to 180 0 [ 180-(75+75)] degrees reason e - ____________________________ f - ____________________________ g - ____________________________ degrees reason h - ____________________________ j - ____________________________ k - ____________________________ Great Marlow School Mathematics Department

10. 35 0 50 0 60 0 x y z a b c 1. degrees reason a - ____________________________ b - ____________________________ c - ____________________________ degrees reason x - ____________________________ y - ____________________________ z - ____________________________ Worksheet 1 2. Great Marlow School Mathematics Department

11. 55 0 d e f 3. 4. degrees reason d - ____________________________ e - ____________________________ f - ____________________________ degrees reason w - ____________________________ x - ____________________________ y - ____________________________ z - _____________________________ 50 0 x y z w Worksheet 2 Great Marlow School Mathematics Department

12. 5. e 30 0 f g 50 0 75 0 degrees reason e - ____________________________ f - ____________________________ g - ____________________________ 6. j k h degrees reason h - ____________________________ j - ____________________________ k - ____________________________ Worksheet 3 Great Marlow School Mathematics Department

13. Date: November 1998 Paper: 4 ----------------------------------------- AB is parallel to CD. (a)i)Write down the size of the angle marked x°. ii)Give a reason for your answer. (2 marks) (b)i)Work out the size of the angle marked y°. ii)Explain how you worked out your answer. (2 marks) [4] Great Marlow School Mathematics Department

14. Date: November 1997 Paper: 3 ----------------------------------------- AC = BC AB is parallel to DC Angle ABC = 52º (a)Work out the value of i)p ii)q The angles marked pº and rº are equal. (b)What geometrical name is given to this type of equal angles? [4] Great Marlow School Mathematics Department