τακης τσακαλακος τραπεζα θεματων γεωμετρια α λυκειου (4ο θεμα)light

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<p> 1. : 2. ( - ) . . H - 2787 3695 3696 3726 4741 4794 4806 5904 13527 - 3721 3728 3729 3903 4307 4583 2788 2789 3825 4588 4622 5900 3701 3702 3723 3812 3954 4555 4616 4651 4735 4781 4821 2799 3700 3704 3722 3926 4571 4603 4643 4814 5908 3715 3813 4652 4798 3705 3727 3803 3817 3906 4567 4614 6875 2809 3694 3697 3699 3717 3720 3762 3784 3789 3904 3915 3932 3938 3945 3948 4579 4593 4640 4649 4783 4810 7433 2792 2797 3691 3711 3713 3735 3741 3747 3751 3754 3777 3806 3808 3811 3815 3908 3961 3994 4559 4562 4565 4611 4635 4762 4786 4791 4795 4797 4799 4801 4802 4803 4808 4816 4818 6876 B - 3725 3732 3745 3757 3796 4606 4619 4646 4731 4812 5898 2794 2802 2808 3693 3698 3703 3706 3709 3718 3724 3734 3737 3739 3765 3775 3798 3810 3820 3822 3824 3911 4569 4599 4626 4630 4645 4648 4650 4653 4655 4737 4765 4767 4769 4771 4774 4778 4788 4790 4792 4796 4832 5886 5902 5911 2806 2810 3714 3759 3767 3781 4756 4804 4822 5910 6879 2796 2804 3731 3771 3787 3793 3800 3919 3966 4753 4757 4793 5895 6878 3. http://drmaths58demo.blogspot.gr 2014 H maths58corfu@gmail.com 2014 http://drmaths58demo.blogspot.gr 4. http://drmaths58demo.blogspot.gr 2 : 4 1 . 5. http://drmaths58demo.blogspot.gr - 1 2787 - . , , , : ) . ( 5) ) , . ( 8) ) 0 + = 180 . ( 12) 5 , , . , , . , . : . . ... 6. - 6 http://drmaths58demo.blogspot.gr ) - , . , = (1) ) , - . : = ( (1)) = ( ) = (2) ) (2) 0 0 + = 180 + = 180 2787 7. http://drmaths58demo.blogspot.gr - 2 3695 - . : : AB = , . ) . ( 10) ) . ( 10) ) . ( 5) 7 : . . ... 8. P(A B) - 8 http://drmaths58demo.blogspot.gr ) : = = ( ) = . ) - , . : = = ( ) = , . ) . 3695 9. http://drmaths58demo.blogspot.gr - 3 3696 xOy 1 2 (, ) (, ) 1 2 &lt; , x , y , . : ) A = BK ( 8) ) , , . ( 8) ) xOy . x y ( 9) 9 , . ( ) , . ( ) , . ( ) , . ... 10. - 10 http://drmaths58demo.blogspot.gr ) 2 1 : = = = ( - - ) = = = (1) ) 2 : = = ( (1)) = ( , = = ) ( - - ) = . ) 2 1 2 : = = = ( - - ) = ( ) = xy . 3696 O A B x y K 1 2 11. http://drmaths58demo.blogspot.gr - 4 3726 , - . A . ) BA , : i) O' . ( 6) ii) . ( 6) ) , : i) KA = KA ( 6) ii) KA + KB &gt; OA + OB ( 7) 11 , , . , , . , . . ... 12. - 12 http://drmaths58demo.blogspot.gr , : = ) i) , , - O' . ii) E 1 2 3 2 1 3 = ( xOy) = () = ) i) , AA, . : = ii) (i) ( = ') + ' &gt; ' + &gt; ' + + &gt; + 3726 2 1 3 13. http://drmaths58demo.blogspot.gr - 5 4741 AB AB &lt; . AB B E AE = . A = AB . E B AK E M . : ) = ( 6) ) = ( 7) ) AK . ( 6) ) AM E . ( 6) 13 , , . , , . , . ( ) , . ( ) , . ( ) , . ... 14. - 14 http://drmaths58demo.blogspot.gr ) : = = () ( - - ) = () = (1) ) = (2), ( = = ) 1 1 : = = ( (1)) ( - - ) = ( (2)) = = . ) = (3), ( = = ) 1 2 : = = () ( - - ) = ( (3)) = . ) ( = ) (), , . 4741 2 1 1 1 15. http://drmaths58demo.blogspot.gr - 6 4794 ( 0 = 90 ) B , . . ) : i) . ( 6) ii) K . ( 7) H E Z iii) . ( 6) ) A , . ( 7) 15 , , . , . : . . ... 16. - 16 http://drmaths58demo.blogspot.gr ) : = = () ( - - ) = () = (1) ) = (2), ( = = ) 1 1 : = = ( (1)) ( - - ) = ( (2)) = = . ) = (3), ( = = ) 1 2 : = = () ( - - ) = ( (3)) = . ) ( = ) (), , . 4794 1 2 1 2 17. http://drmaths58demo.blogspot.gr - 7 4806 , . . . ) : i) = ( 8) ii) = ( 9) ) , - , ,. ; . ( 8) 15 , . : . . , . ( ) , . ( ) , . ( ) ... 18. - 18 http://drmaths58demo.blogspot.gr ) i) : = = ( ) - = . ii) 1 2 : = = ( ) 2 = ( ) = . ) : = = ( ) = , . 4806 1 2 19. http://drmaths58demo.blogspot.gr - 8 5904 A, B, , E . E B, A . ) : i) A B . ( 5) ii) AB , - . ( 5) iii) B A . ( 8) ) A A . ( 7) 17 , , . . . . . , . ( ) , . ( ) , . ( ) ... 20. - 20 http://drmaths58demo.blogspot.gr ) i) 1 2 : = () = () ( - - ) = () = . = = = . ii) ' = ( , , ' ) , . || . iii) ' , . , = . ) A , A . A A . 5904 K 1 2 21. http://drmaths58demo.blogspot.gr - 9 13527 , . : : = , , . ) . ( 10) ) . ( 10) ) , , . ( 5) 21 , . ( ) , . ( ) , . ( ) . . . . ... 22. P(A B) - 22 http://drmaths58demo.blogspot.gr ) : = = ( ) = ( ) ( - - ) = ) , , . , , - , , : || - . = , ( ) = = . ) . 13527 23. http://drmaths58demo.blogspot.gr 2 : 4 2 . 24. H 25. 25 http://drmaths58demo.blogspot.gr ( = ) . - . : ) = ( 8) ) . ( 9) ) = ( 8) , . ( ) , . ( ) , . ( ) ... 1 0 3721 26. 26 http://drmaths58demo.blogspot.gr ) 1 11 1 = ( - ) || ' = ( - ) = || ' = ( ) , = (1) = (1 ) = - = - = ) : = = ( ) ( - - ) = ( , = ) 11 1 1 11 = (2) = (3) ( = ) : = ' () = ( (2)) = ( ( - - ) (3)) = (4) ) = (4 ) = + = + = 3721 11 1 1 27. 27 http://drmaths58demo.blogspot.gr (O, ) , . ) : i) = + ( 6) ii) - = - ( 8) ) A = BE , i) . ( 6) ii) , . ( 5) . (, ) - . , . ... 1 1 3728 28. 28 http://drmaths58demo.blogspot.gr ) . = = = i) = + = + ii) = + = = = = - , = (1) ) i) = + = + = . ii) = ( ) (, ) ( = = = ), . , , . ( (, ) - . , ) , , , . 3728 29. 29 http://drmaths58demo.blogspot.gr . . . . : ) . ( 10) ) = ( 8) ) PA + PB . ( 7) , . . (, ) - . 1 2 3729 ... 30. 30 http://drmaths58demo.blogspot.gr ) , - , - , - . , , - ( ) . = (1) ) ( = (2) ) . (1 ) (2 ) = - = - = ) = (3) = (4) . : (3) (4 ) = + + = + + + = ( + ) + ( + ) = + 1 3729 2 31. http://drmaths58demo.blogspot.gr 1 3 3903 AB = = . , : ) . ( 7) ) = ( 9) ) || . ( 9) 31 , . ( ) , . ( ) , . ( ) , . ... 32. 32 http://drmaths58demo.blogspot.gr 1 1 2 2 : = : = (1) = ( ) : = (2) ) 1 2 : = = () ( - - ) = ( ) = . ) 2 2 = : = = ( (1)) ( - - ) = ( (2)) = + = + = ) ( = ) ( = ) , - . 11 = - , ' . . 3903 2 1 1 2 3 3 1 2 1 33. 33 http://drmaths58demo.blogspot.gr , . () - . - (). ) . ( 8) ) , : = = . ( 8) ) : + = . ( 9) , . : . . , . ... 1 4 4307 34. 34 http://drmaths58demo.blogspot.gr ) , , , || || 12 22 = ( ) (1) = ( ) (2) = = , . 11 21 = ( ) (3) = ( ) (4) (1), (3) : 1 2 = . (2), (4) : 1 2 = . ) 1 2 1 2 , : = = = = = , : = = = ) () : (+) = + = + + = = 4307 1 2 21 1 2 35. http://drmaths58demo.blogspot.gr 1 5 4583 AB &lt; , . , . : ) . ( 8) ) = ( 9) ) = = ( 8) 35 , . ( ) , . ( ) , . ( ) , . , . , . ... 36. 36 http://drmaths58demo.blogspot.gr ) 1 2 1 2 2 2 = ( ) || ' = ( - ) || ' = ( ) = (1) || 1 2 1 ' = ( ) ( =) = () = (2) (1) (2) . ) 1 1 2 : = ( ) = ( ) || = () ( - - ) = . ) AE = AZ = A = - 4583 1 2 21 1 1 2 37. http://drmaths58demo.blogspot.gr 2 : 4 3 . 38. http://drmaths58demo.blogspot.gr/ H 39. http://drmaths58demo.blogspot.gr 1 6 2788 ( 0 = 90 ), 0 = 50 , , = . - . ) : i) . ( 6) ii) 0 = 10 ( 10) 500 ) . ( 9) 39 2 . , . 1 . , , . ... 40. 40 http://drmaths58demo.blogspot.gr ) i) ( = ) . , = - . ii) : 0 0 1 = 90 0 2 1 0 0 0 0 0 0 = = 50 = 180 - 2 90 - = 180 - 100 = 90 - 80 = 10 ) 0 0 2 1 0 0 0 0 1 12 2 = 90 = = 50 () = 90 - = 90 - 50 = 40 ( , ) 2788 50 0 1 50 0 2 2 1 41. http://drmaths58demo.blogspot.gr 1 7 2789 , . Ax || (, ). Ax = . : ) . ( 7) ) . ( 9) ) . ( 9) 41 , . . . . . , . . ... 42. 42 http://drmaths58demo.blogspot.gr ) || = , - - , . , - . ) 1 1 2 = 2 = ( , || ' ) = = 2 . ) = 2 = + 2 = + = . 2789 x M B 1 2 43. http://drmaths58demo.blogspot.gr 1 8 3825 &lt; . AK , . : ) 0 = 90 + 2 ( 7) ) = ( 8) ) - = 2 ( 10) 43 . 2 . , , . , , . ... 44. 44 http://drmaths58demo.blogspot.gr ) 1 2 = = 2 ( ) - , 0 2 0 = 90 + = 90 + 2 ) , . . , = . ) () 0 0 : + + = 180 + + 90 + 2 0 = 90 + 2 + + 2 2 - = - = 2 2 2 3825 1 2 45. http://drmaths58demo.blogspot.gr 1 9 4588 ( ) , B = , ( ) , E = B . , . ) . ( 8) ) . ( 12) ) AB || Z . ( 5) 45 : . . , , . 2 . , ... 46. 46 http://drmaths58demo.blogspot.gr ) : 0 = = = 60 = = = : 0 1 0 0 = 120 (180 - 60 ) : 0 1 = = 30 : 0 0 0 = 120 (180 - 60 ) : 0 2 1 = = 30 ) 0 0 0 0 1 0 1 2 = 60 + = 60 + 60 = 90 : = = () : = = 60 (1) = (2) = = , , , - . ) 0 1 = = 60 , ' . , || . 4588 60 0 60 0 60 0 21 1 1 2 1 1 47. http://drmaths58demo.blogspot.gr 2 0 4622 . , , = 2 . Z || : ) . ( 10) ) . ( 5) ) AE = 2 . ( 5) ) 3A...</p>

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