SIMILAR TRIANGLES [ X ] 1

             YASH     CLASSES

    

            1. SIMILAR TRIANGLES    [  X  ]

    1 .The perpendicular  AD  , on the base 

        BC  of a Δ ABC , intersect  BC at D , so that 

         BD = 3CD.Prove that  , 2 AB² =  AC²   + BC²  .

   2 . Prove that   three  times  the square  of any  

       side  of  an equilateral  triangle  is equal to

       four times The square  of  its altitude .

   3.  In a rectangle  ABCD  , there is a point    

        which  is joined to each  of the  vertices

        A , B, C and D . Prove that  

          OA²  + OC²  =  OB²  + OD².

   4 .  In  any Δ ABC  AB = AC  and  D is any  

    point  BC . Prove that AB²  -AD ²  = BD x CD .

  5. Write  Thales theorem  . prove it .

  6. Write converse of  Thales theorem . prove it.    

 7. Write  Pythagoras theorem . prove   it .

 8. Write converse of Pythagoras  and  prove it .

 9. Write area  ratio theorem and prove  it .

10. P and  Q  are  the  mid  points  of  the

      sides  AC  and  BC  respectively  of  a

      triangle  ABC , right  angle  at  C .

      Prove  that ,  [a ] 4 AQ ²  =  4 AC ²  + BC².

              [ b ] 4 [AQ ²  + BP ²  ] = 5 AB² .

 11. Using  similar triangles , prove that the line

       drawn  from midpoint  of  one side of triangle

       parallel to another side bisect the side .