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EVERYTHING YOU NEED TO KNOW TO GET A GRADE C GEOMETRY & MEASURES (FOUNDATION) Part 1

EVERYTHING YOU NEED TO KNOW TO GET A GRADE C GEOMETRY & MEASURES (FOUNDATION) Part 1. Rhombus. Trapezium. Rectangle. Rhombus. Rhombus. Parallelogram. Rhombus. Trapezium or Right-angle Trapezium. 110°. 250°. Base angles in a kite are equal. Opposite angles in a rhombus are equal.

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EVERYTHING YOU NEED TO KNOW TO GET A GRADE C GEOMETRY & MEASURES (FOUNDATION) Part 1

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  1. EVERYTHING YOU NEED TO KNOW TO GET A GRADE C GEOMETRY & MEASURES (FOUNDATION) Part 1

  2. Rhombus Trapezium Rectangle Rhombus

  3. Rhombus

  4. Parallelogram Rhombus Trapezium or Right-angle Trapezium

  5. 110° 250° Base angles in a kite are equal Opposite angles in a rhombus are equal Angles around a point sum to 360° Angles in a kite sum to 360° 30

  6. Kite Trapezium

  7. Replace a with 3 and b with 5.2 P = 2 x 3 + 2 x 5.2 P = 6 + 10.4 16.4 Total areas of both shapes are equal to one as shown.

  8. Equilateral triangle Rhombus 2 (Fits on top of itself twice through a full turn)

  9. Can choose either as your answer 5cm 5cm 3cm 3cm 9cm 5cm Any two of rectangle, parallelogram, kite or arrowhead The 3cm and 5cm rods would not meet when joined with the 9cm rod.

  10. In an isosceles triangle, the base angles are the same Angles in a triangle sum to 180° 20 80 50 50 Each angle is 60° in an equilateral triangle 120° because angles on a straight line add to 180° 30° because angles in a right angle add to 90° Base angles are both 30° so ABD is an isosceles triangle

  11. Isosceles Triangle Angles in a triangle add to 180° 35° 73° 107° 73° 107° because angles on a straight line add up to 180° 146° ÷ 2 = 73° 180° - 34° = 146° 73 y = 180° - 107° - 38° = 35° 35 No, because 38° is not equal to 35°. Therefore, it is not an isosceles triangle

  12. Angles in a triangle add to 180° 153° 27° 27° 54° ÷ 2 = 27° 180° - 126° = 54° 153° because angles on a straight line add up to 180° 27 153

  13. Base angles are the same in an isosceles triangle 80° Means work out angle A in triangle ABC Means work out angle R in triangle PQR Angles in a triangle add to 180° 180° - 80° - 80° = 20° 20 Base angles are the same in an isosceles triangle 65° 65° 70° 50° 40° Angles in a triangle add to 180° 180° - 70° - 70° = 40° A right angle is 90° 90° - 40° = 50° 65 Both base angles are equal 130° ÷ 2 = 65° 180° - 50° = 130°

  14. 132° ÷ 2 = 66° 180° - 48° = 132° Angles on a straight line add to 180° 180° - 66° = 114° 114° 66° 66° 114 A quadrilateral is made up of two triangles 180° Angles is a triangle add up to 180° 180° + 180° = 360° 180°

  15. LEARN OFF BY HEART (because the exterior angles add up to 360°) Exterior angle = 72° Two exterior angles joined together 72° As worked out in part (a) 72° 144

  16. All the angles and sides are the same in a regular pentagon Exterior angle LEARN OFF BY HEART 72° Exterior angle 72° 36° Interior angle 108° Exterior angle 72° 36° Exterior angle 72° Exterior angle 72° = 72° Angles on a straight line add up 180° Interior angle = 180° - 72° = 108° Base angles in a isosceles triangle are the same 180° - 108° = 72° 36

  17. LEARN OFF BY HEART Interior angle Exterior angle Angles on a straight line add up 180° Exterior angle = 180° - 162° = 18° = 20 20

  18. LEARN OFF BY HEART Decagon Pentagon Interior angle 108° Interior angle 144° Sum of interior angles = (number of sides – 2) x 180° 108° 36° 36° 144° Sum of interior angles of an decagon = (10 – 2) x 180° = 8 x 180° = 1440° = 144° Sum of interior angles of a pentagon = (5 – 2) x 180° = 3 x 180° = 540° = 108° Angles around a point add up to 360° 360° - 144° - 108° = 108° Base angles in a isosceles triangle are the same 72° ÷ 2 = 36° 180° - 108° = 72° Therefore, ABC lie on a straight line (Angles on a straight line add up to 180°) = 180° 144° + 36°

  19. LEARN OFF BY HEART Sum of interior angles = (number of sides – 2) x 180° Hexagon Interior angle 120° Square 60° 60° Square 60° Sum of interior angles of an hexagon = (6 – 2) x 180° = 4 x 180° = 720° = 120° Angles around a point add up to 360° 360° - 120° - 90° - 90° = 60° Base angles are the same 180° - 60° = 120° 120° ÷ 2 = 60° Therefore, as all angles are 60° AHJ is equilateral

  20. Sum of interior angles of an octagon = (8 – 2) x 180° = 6 x 180° = 1080° = 135° Sum of interior angles = (number of sides – 2) x 180° LEARN OFF BY HEART 135 135° 135° 135° 135° 135° 135° 135° 135° As worked out in part (a) = 135° Angles around a point add up to 360° 360° - 135° - 135° = 90° Therefore, as all angles are 90° PQRS is a square

  21. -1 2.5

  22. 70° 40° 70° Alternate angles are equal Angles on a straight line add up 180° 180° - 110° = 70° Angles in a triangle add up 180° 180° - 40° - 70° = 70° As both base angles are 70°, triangle BEF is isosceles.

  23. 55° 55° Alternate angles are equal Angles in a triangle add up 180° 180° - 70° - 55° = 55° As both base angles are 55°, triangle ABC is isosceles.

  24. 41° 113° 41 Interior angles add up to 180° 180° - 67° = 113° 113

  25. 2 6cm 6cm 4cm 2cm 2cm 3cm 3cm OTHER ANSWERS ALSO ALLOWED 4cm Perimeter is the length around a shape 14cm Perimeter of rectangle A = Difference = 16cm - 14cm 16cm Perimeter of rectangle B = 2

  26. Perimeter is the length around a shape 6cm 4cm 4cm 6cm 6cm + 4cm + 6cm + 4cm Perimeter of rectangle = 20 Square has 4 equal sides 3cm for each side

  27. OTHER ANSWERS ALSO ALLOWED x x x x Because two lengths of 12cm makes 24cm which is more than the perimeter As evident from the rectangle drawn for part (a)

  28. 40cm 20cm 8cm 10cm 5cm 1cm 4cm 2cm 1cm 2cm 4cm 5cm 10cm 20cm 40cm 8cm Find the only rectangle which has a perimeter of 26cm 8 5

  29. Kilo means a thousand 1km = 1000m 1000m Area = Length x Width = 1000m x 10m Split compound shape into two rectangles Rectangle A 200m Rectangle B Area of rectangle A = 100 x 30 200a + 3000 = 10000 Area of rectangle B = 200 x a 35 200a = 7000

  30. Count the number of squares to find the area C E B

  31. Shaded Area = Area of square – Area of circle 30cm Diameter LEARN THE FORMULAE OFF BY HEART Area of square = length x width = 80cm x 80cm Area of circle = = 3.14 x 30cm x 30cm Area shaded = 6400 - 2826 3574

  32. equal to (because the length around the shape is the same) less than (because more than half the rectangle is unshaded)

  33. 10cm 10cm Shaded Area = Area of big square ABCD – Area of the 4 congruent (identical) triangles length x width Area of big square = = 10cm x 10cm Area of one triangle = Area of one triangle = Area of one triangle = Shaded area = Area of four triangles = 82

  34. Area of small square = 30cm x 30cm 900 Length of large square = 50 300cm x 180cm Area of floor = Number of small tiles needed = Number of small tiles needed = 60

  35. Perimeter B = 9cm Perimeter A = 10cm Perimeter is the length around a shape 2cm 2cm 2cm 2cm Perimeter C = 10cm 2cm + 2cm + 2cm + 2cm Perimeter of D = 8 A and C Area is the space inside a shape C and D

  36. Shaded Area = Area of big square – Area of two smaller squares length x width Area of big square = = 12cm x 12cm Area of one small square = length x width = 4cm x 4cm Area of both squares = Shaded Area = length x width Area of big square = Area of one small square = length x width Area of both squares = Shaded Area = Fraction shaded = Unshaded

  37. 6

  38. A, B and E

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