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

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

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

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

+ d = 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 ab cd ef g h a + d = Why? If we substitute e for a in the first statement we have….. a e Great Marlow School Mathematics Department

= 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 b = - b a = c Great Marlow School Mathematics Department

degrees reason x alternate angles y alternate angles z adjacent angles – straight line ((180 – (50+60)) degrees reason a - ____________________________ b - ____________________________ c - ____________________________ x y z a b c 1. degrees reason a adjacent angles – straight line. (180 – 35) b vertically opposite angles c 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

Find the sizes of the angles marked with letters. You must give a reason for your answer d e f degrees reason d Angles between parallel lines add up to e Angles at a point add up to [360- (125+90)] f Angles between parallel lines add up to degrees reason w Vertically opposite angles are equal. x – 50 0 Alternate angles are equal y Angles in a triangle add up to [180-(50+90)] z 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

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

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

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

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

Date: November 1998 Paper: 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

Date: November 1997 Paper: 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