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SAI International School
                                                      CLASS - X

               Mathematics
               CHAPTER-6: Triangles-4

               HOME ASSIGNMENT-4


               SUBTOPIC :Pythagoras Thm& Its Converse

                   1.    B of ∆ABC is an acute angle and AD      BC.
                       Prove that AC  = AB  + BC  - 2BC . BD.
                                    2
                                           2
                                                  2

                                                                           2
                                                                                           2
                                                                                   2
                   2.  In     ABC,   C is an obtuse angle. AD    BC and AB   = AC   +3BC . Prove that
                       BC = CD.


                                                                                   o
                                                                o
                   3.  In a quadrilateral ABCD, where    B = 90  and     ACD = 90  prove that
                                2
                                       2
                       AD  = AB  + BC  + CD
                          2
                                              2

                   4.  If the diagonal BD of a quadrilateral ABCD bisects both       B and    D, show


                       that   =



                   5.  O is any point inside a triangle ABC. The bisector of     AOB,    BOC ,and
                       COA meet the sides AB, BC and AC in points D, E and F respectively. Show that
                       AD x BE x CF = DB x EC x FA

                   6.  AD is a median of ∆ABC . The bisector of   ADB and     ADC meet AB and AC in E
                       and F respectively. Prove that EF II BC.
























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