Page 94 - Mathematics Coursebook
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8.4 Symmetry properties of triangles, special quadrilaterals and polygons



               8.4  Symmetry properties of triangles, special quadrilaterals and
                     polygons


               You should know these symmetry properties of triangles, quadrilaterals and some regular polygons.



                       A scalene triangle has:        An isosceles triangle has:     An equilateral triangle has:
                       s  DIFFERENT LENGTH SIDES      s    SIDES THE SAME LENGTH     s  ALL SIDES THE SAME LENGTH
                       s  DIFFERENT SIZE ANGLES       s    ANGLES THE SAME SIZE      s  ALL ANGLES THE SAME SIZE
                       s  NO LINES OF SYMMETRY
                                                                                     s    LINES OF SYMMETRY
                  Triangles  s  ORDER   ROTATIONAL SYMMETRY   s  ORDER   ROTATIONAL SYMMETRY   s  ORDER   ROTATIONAL SYMMETRY
                                                      s    LINE OF SYMMETRY






                       A square has:                  A rectangle has:               A rhombus has:
                       s  ALL SIDES THE SAME LENGTH   s    PAIRS OF EQUAL LENGTH SIDES  s  ALL SIDES THE SAME LENGTH
                       s    PAIRS OF PARALLEL SIDES   s    PAIRS OF PARALLEL SIDES   s    PAIRS OF PARALLEL SIDES
                       s  ALL ANGLES   —              s  ALL ANGLES   —              s  OPPOSITE ANGLES EQUAL
                       s    LINES OF SYMMETRY         s    LINES OF SYMMETRY         s    LINES OF SYMMETRY
                       s  ORDER   ROTATIONAL SYMMETRY   s  ORDER   ROTATIONAL SYMMETRY   s  ORDER   ROTATIONAL SYMMETRY





                       A parallelogram has:           A trapezium has:               An isosceles trapezium has:
                       s    PAIRS OF EQUAL LENGTH SIDES  s  DIFFERENT LENGTH SIDES   s    SIDES THE SAME LENGTH
                  Quadrilaterals  s  OPPOSITE ANGLES EQUAL  s  DIFFERENT SIZED ANGLES  s    PAIRS OF EQUAL ANGLES
                                                                                     s    PAIR OF PARALLEL SIDES
                       s    PAIRS OF PARALLEL SIDES
                                                      s    PAIR OF PARALLEL SIDES
                                                      s  NO LINES OF SYMMETRY
                                                                                     s    LINE OF SYMMETRY
                       s  NO LINES OF SYMMETRY
                                                      s  ORDER   ROTATIONAL SYMMETRY
                                                                                     s  ORDER   ROTATIONAL SYMMETRY
                       s  ORDER   ROTATIONAL SYMMETRY

                       A kite has:
                       s    PAIRS OF EQUAL LENGTH SIDES
                       s  NO PARALLEL SIDES
                       s    PAIR OF EQUAL ANGLES
                       s    LINE OF SYMMETRY
                       s  ORDER   ROTATIONAL SYMMETRY





                  Regular polygons   A regular pentagon has:  A regular hexagon has:  A regular octagon has:
                       s    SIDES THE SAME LENGTH
                                                                                     s    SIDES THE SAME LENGTH
                                                      s    SIDES THE SAME LENGTH
                       s    LINES OF SYMMETRY
                                                      s    LINES OF SYMMETRY
                                                                                     s    LINES OF SYMMETRY
                                                                                     s  ORDER   ROTATIONAL SYMMETRY
                                                      s  ORDER   ROTATIONAL SYMMETRY
                       s  ORDER   ROTATIONAL SYMMETRY
                                                                                     s    ANGLES THE SAME SIZE
                       s    ANGLES THE SAME SIZE
                                                      s    ANGLES THE SAME SIZE
                                                                                                        8 Symmetry      93
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