Wk 30 Geometry[1]

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Wk 30 Geometry[1]

  1. 1. GCSE Mathematics Geometry
  2. 2. Types Of Triangle <ul><li>Isosceles Right angle </li></ul><ul><li>Equilateral Scalene </li></ul>
  3. 3. Types of quadrilateral <ul><li>Square Rectangle Rhombus </li></ul><ul><li>Kite Parallelogram Trapezium </li></ul>
  4. 4. Other Shapes <ul><li>5 sides Pent agon </li></ul><ul><li>6 Sides Hex agon </li></ul><ul><li>7 Sides Hept agon </li></ul><ul><li>8 Sides Oct agon </li></ul><ul><li>9 Sides Non agon </li></ul><ul><li>10 Sides Dec agon </li></ul>
  5. 5. Angles <ul><li>Angles about a point = 360° </li></ul><ul><li>Angles on a straight line = 180° </li></ul><ul><li>Angles in a triangle =180° </li></ul><ul><li>Angles in a quadrilateral = 360° </li></ul><ul><li>Angles in a n sided shape = </li></ul><ul><li>(n-2)x180° </li></ul>
  6. 6. Parallel Lines <ul><li>a b </li></ul><ul><li>c d </li></ul><ul><li>e f </li></ul><ul><li>g h </li></ul><ul><li>a=d=e=h b=c=f=g </li></ul>
  7. 7. Bearings <ul><li>All bearings are taken CLOCKWISE from the north </li></ul><ul><li>All bearings are quoted as 3 digit figures </li></ul>
  8. 8. Bearings <ul><li>b a </li></ul><ul><li>7 ° 35 ° </li></ul><ul><li>a = 035° </li></ul><ul><li>b = 353° </li></ul><ul><li>a </li></ul><ul><li>55° b </li></ul><ul><li>b from a </li></ul><ul><li>= 125° </li></ul><ul><li>a from b </li></ul><ul><li>= 305° </li></ul>
  9. 9. Geometrical Movement <ul><li>Translation: Movement left and right, and up and down </li></ul><ul><li>Reflection: Mirror image produced about a given line </li></ul><ul><li>Rotation: Movement by a given number of degrees, about a point </li></ul><ul><li>Enlargement: Made a number of times larger or smaller, about a given point. </li></ul>
  10. 10. Geometrical Movement <ul><li>A to B: </li></ul><ul><li>Reflection in y axis </li></ul><ul><li>A to C: </li></ul><ul><li>Translation 3 1 </li></ul><ul><li>A to D: </li></ul><ul><li>Rotation , 180° about(-0.5,0) </li></ul>A C D B
  11. 11. Enlargement <ul><li>to </li></ul><ul><li>Enlargement scale factor 2 </li></ul><ul><li>to </li></ul><ul><li>Enlargement Scale factor 4 </li></ul><ul><li>to </li></ul><ul><li>Enlargement Scale factor 0.5 </li></ul>
  12. 12. Similarity and Congruence <ul><li>Two (or more) shapes are said to be congruent if they are exactly the same. </li></ul><ul><li>Two or more shapes are said to be similar if one is an enlargement of the other. </li></ul>
  13. 13. Similarity and Congruence <ul><li>A B C D </li></ul><ul><li>A and B are congruent </li></ul><ul><li>A and C, B and C are similar </li></ul>
  14. 14. Similar Triangles <ul><li>7 </li></ul><ul><li>x </li></ul><ul><li>6 </li></ul><ul><li>26 </li></ul><ul><li>As the triangles are similar, the ratio of compared sides will be the same </li></ul><ul><li>x/7 =26/13 </li></ul><ul><li>x=14 </li></ul>

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