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    6.  In the given figure, it is given that LM = MN,     9.  If OA = OB, OC = OD and ∠AOB = ∠COD, then
                         QM = MR, ML ⊥ PQ and MN ⊥ PR. Then ∠PQR             which of the following pairs is true?
                         is equal to                (Critical Thinking)                                  (Decomposition)
                                            P
                                                                                                  O

                                       L         N

                                    Q                                                        C    P     D
                                                                                       A
                               (a)  ∠PLM            (b)  ∠QPR
                                                                                                   B
                               (c)  ∠NRM            (d)  ∠MNP
                                                                                    (a)  ∠OCP = ∠OPC
                      7.  ABCD is a straight line, with AB = BC = CD. P is
                         a point not on the straight line, such that PB =           (b)  OC = CD
                         PC. Which of the following statements is true?
                                                    (Critical Thinking)             (c)  OA = CD
                                            P
                                                                                    (d)  AC = BD
                                                                         10.  24.  In  the given figure,  ABC  is an isosceles
                                                                             triangle in which AB = AC. If E and F be the
                               A        B        C       D
                                                                             midpoints of AC and AB respectively, then BE
                               (a)  PA = PB         (b)  PB = PD             is equal to            .   (Critical Thinking)
                                                                                                A
                               (c)  PA = PD         (d)  None of these
                      8.  A 4 x 4 grid of squares is drawn. How many                        F       E
                         squares  of any size  can be found that  are
                         congruent to a 2 x 2 square?                                    B             C
                                                (Algorithmic Thinking)
                                                                                    (a)  AB             (b)  CE
                               (a)  4               (b)  9
                                                                                    (c)  CF             (d)  BF
                               (c)  16              (d)  25

                                       Ravi and Priya are working on designing identical triangular flags for a school
                                       event. Each flag is a triangle with all sides measured in centimeters.

                                       Flag designed by Ravi (DABC):            Flag designed by Priya (DPQR):
                                          AB = 12 cm          A                                 P
                                          BC = 16 cm                                       3x cm        6x – 4
                                          AC = 20 cm      12 cm       20 cm
                                                              B            C                   Q    3x + 4   R
                                                                  16 cm
                                       If DABC ≅ DPQR , what is the value of x? Also, what is the perimeter (in cm) of
                                       each flag?

                                             (a)  x = 4, Perimeter = 48 cm          (b)  x = 5, Perimeter = 6 cm

                                             (c)  x = 6, Perimeter = 72 cm          (d)  x = 7, Perimeter = 80 cm

                                                                                                Geometric Twins       41

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