Teach GCSE Maths Trapezia

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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

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   = 360 

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   = 360 

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   = 360 

trapezium a 100  b e.g. Find a and b. 140 

trapezium 100  + a = 180  a 100  b e.g. Find a and b. so, a = 80  140 

trapezium 100  + a = 180  a 100  b e.g. Find a and b. so, a = 80  140  140  + b = 180  so, b = 40 

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

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:

Examples 112  c d e c = 180   112  e = c ( isosceles trapezium ) = 68  d = 112  ( isosceles trapezium ) 2.Find the marked angles:

SUMMARY  A trapezium is a quadrilateral with 1 pair of parallel sides. a + b = 180º b a c d c + d = 180º  In an isosceles trapezium, the non-parallel sides are equal. There are 2 pairs of equal angles b a a b

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 