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Teach GCSE Maths Trapezia Slide 2 Christine Crisp "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages" Trapezia Slide 3 A trapezium is a special type of quadrilateral: a quadrilateral with 1 trapezium N.B. 1 trapezium but 2 trapezia A quadrilateral has 4 straight sides. pair of parallel sides Slide 4 Tell your partner what you know about the sum of the interior angles of a trapezium. Ans: Since it is a type of quadrilateral, the sum is 360 . 120 60 e.g. 105 75 ALSO, the sum of each pair of angles between the parallel lines is 180 . 120 + 60 + 75 + 105 = 360 Slide 5 120 Tell your partner what you know about the sum of the interior angles of a trapezium. Ans: Since it is a type of quadrilateral, the sum is 360 . 60 e.g. 105 75 ALSO, the sum of each pair of angles between the parallel lines is 180 . 120 + 60 = 180 120 + 60 + 75 + 105 = 360 Slide 6 120 Tell your partner what you know about the sum of the interior angles of a trapezium. Ans: Since it is a type of quadrilateral, the sum is 360 . 60 e.g. 105 75 ALSO, the sum of each pair of angles between the parallel lines is 180 . 120 + 60 = 180 105 + 75 = 180 120 + 60 + 75 + 105 = 360 Slide 7 trapezium a 100 b e.g. Find a and b. 140 Slide 8 trapezium 100 + a = 180 a 100 b e.g. Find a and b. so, a = 80 140 Slide 9 trapezium 100 + a = 180 a 100 b e.g. Find a and b. so, a = 80 140 140 + b = 180 so, b = 40 Slide 10 If the non-parallel sides are equal we have an isosceles trapezium What can you suggest about the angles? isosceles ANS: There are 2 pairs of equal angles b b aa trapezium Slide 11 42 a b Examples 1.Find the marked angles: a = 180 90 ( 4 th angle of quadrilateral ) = 138 = 90 Either: b = 180 42 = 138 b = 360 90 90 42 Or: Slide 12 Examples 112 c d e c = 180 112 e = c ( isosceles trapezium ) = 68 d = 112 ( isosceles trapezium ) 2.Find the marked angles: Slide 13 SUMMARY A trapezium is a quadrilateral with 1 pair of parallel sides. a + b = 180 b a c d c + d = 180 In an isosceles trapezium, the non-parallel sides are equal. There are 2 pairs of equal angles b a a b Slide 14 Exercise 1.Find the marked angles: 61 110 a b ANS: a = 180 61 b = 180 110 = 70 c = 180 100 e = c ( isosceles trapezium ) = 80 = 119 = 80 d = 100 ( isosceles trapezium ) d c e 100 Slide 15