Geometry:Discussion of Shapes

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