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    6. If the angles of a triangle are in the ratio 1 : 2 : 7,   the  entire  set  is  composed  of only  three
                         then the triangle is a/an       .                   distinct geometric species. To prove this, you
                                                 (Analytical Thinking)       must  analyse the  properties  of the  pieces
                                                                             (angles and side  relationships).If you  were
                                (a)  Acute-angled triangle                   to  categorize  these  7 pieces  based  on their
                                                                             geometric  shape  name  (regardless  of their
                                (b)  Obtuse-angled triangle
                                                                             size), which of the following represents  the
                                (c)  Right-angled triangle                   correct classification of the set?
                                                                                                    (Pattern Recognition)
                                (d)  Right-angled isosceles triangle
                                                                                    (a)   The Trio: 5 Isosceles Right Triangles,
                      7.  You have discovered a digital vault protected                1 Square, and 1 Parallelogram.
     computational thinking quest  by  a  “Symmetry  Key.”  The  key  is  a  perfect
                         6-pointed star (a Hexagram) formed by two                  (b)   The Spectrum: 7 Unique shapes
                         overlapping,  congruent  equilateral  triangles               that cannot be mapped to one
     Tick ( ) the correct option.  centered  on the  same  point.  To unlock  the      another.
                         vault, you must rotate the star until it perfectly         (c)   The Binary: 6 Triangles and 1
                         aligns with its original “resting state.” However,            Quadrilateral.
                         the vault’s  computer  is programmed  to  be
                         efficient: it only accepts the smallest positive           (d)   The Scale: 5 Triangles of different
                         rotation  that  results  in  an identical  visual             angles, 1 Rhombus, and 1
                         configuration.                                                Rectangle.
                         What  is the  rotational symmetry  of this      10.  For the “Eyes” construction,        A
                         created star (Hexagram)?  (Critical Thinking)       as shown adjacent if points
                                                                             A and B are the centers for
                                (a)  30°            (b)  60°                 the  upper  and  lower arcs   X           Y
                                                                             for the  EYE,  what  must            B
                                (c)  90°            (d)  120°                be true for  the EYE  to  be
                      7.  If you place four equilateral triangles around a   symmetrical?
                         single point, what is the “gap angle” remaining               (Logical Thinking)
                         to complete the 360°?    (Abstract Thinking)
                                                                                    (a)  AX = AY and BX = BY
                                (a)  30°            (b)  60°

                                                                                    (b)  AX = BX and AY = BY
                                (c)  90°            (d)  120°
                      9.  You  are  given  a  standard  7-piece  Tangram            (c)  AX = AY = BX = BY
                         set. A master designer claims that although
                         there  are  7 physical  pieces,  the  “DNA” of             (d)  AB = XY

                                          An 8 × 8 chessboard has two squares of the same colour removed (the top-left
                                         and bottom-right corners, both white). You have 31 dominoes, each covering
                                         exactly two squares (2 × 1). Is it possible to tile the remaining 62 squares
                                         perfectly?

                                                (a)  No, the grid is no longer a perfect square.

                                                (b)  Yes, we can place the tiles diagonally.

                                                (c)  No, because every domino must cover one white one black square.

                                                (d)  Yes, because 62 is an even number.

                                                                                           Construction and Tilings   51

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