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hba

My tutorial on plane geometry.

  • one year ago
  • one year ago

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  1. hba
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    \[\Huge{\color{gold}{\star \star \star}\color{red}{\text{Plane Geometry}}}\] \[ \underline {ANGLE}:An \ angle \ is \ formed \ by \ two \ lines \ or \ line \ segments \ intersecting \ at \ a \ point. \]\[The \ point \ of \ intersection \ is \ called \ vertex .Unit \ of \ Angle \ is \ taken \ as\ degrees.\]\[Angle \ is \ obtained \ by \ intersection \ of \ two \ lines \ AB \ and \ BC \ is \ denoted \ by \ < ABC. \]\[We \ can \ also \ write \ <B \ for <ABC.\]|dw:1357729031105:dw|

    • one year ago
  2. hba
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    \[TYPES \ OF \ ANGLES:\]|dw:1357729201753:dw|

    • one year ago
  3. hba
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    \[PROPERTIES \ RELATED \ TO \ LINES \ AND \ ANGLES:\] \[\underline {1}:The \ \sum \ of \ measure \ of \ the \ angles \ at \ a \ point \ on \ one \ straight \ line \ is \ 180^0\] |dw:1357729712082:dw|

    • one year ago
  4. hba
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    \[\underline {2}:Sum \ of \ all \ angles \ about \ a \ point \ is \ 360 ^0 \]|dw:1357729894167:dw|

    • one year ago
  5. hba
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    \[\underline{3}:Two \ lines \ l \ and \ m \ are \ perpendicular \ if \ they \ intersect \ at \ 90^0.We \ write \ this \ as \ l \ perp \ m \]|dw:1357730164742:dw|

    • one year ago
  6. hba
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    \[\underline{4}:Shortest \ distance \ \between \ two \ lines \ or \ a \ point \ and \ a \ line \ is \ always \ perpendicular \ distance.\]\[\underline{5}: If \ the \ \sum \ of \ two \ angles \ is \ 180^0 \ they \ are \ called \ supp \ angles.\]\[\underline{6}:If \ the \sum of \ two \ angles \ is \ 90^0 \ they \ are \ called \ comp \ angles.\]

    • one year ago
  7. hba
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    \[\underline{7}:If \ two \ lines \ intersect,opposite \ angles \ formed \ \ are \ called \ vertical \ \]\[angles \ and \ they \ are \ always \ equal. \] \[In \ figure \ : a=c \space and \ c=d\]|dw:1357730912103:dw|

    • one year ago
  8. hba
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    \[\Huge --- \text{END TO ANGLES}---\]

    • one year ago
  9. hba
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    \[\underline{TRIANGLE}:A \ closed \ figure \ with \ three \ angles \ and \ three \ straight \ sides\]\[is \ called \ a \ \triangle.\]

    • one year ago
  10. hba
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    \[PROPERTIES \ AND \ DEFINITIONS \ OF \ A \ TRIANGLE:\]\[\underline{1}:Sum \ of \ interior \ angles \ of \ a \ \triangle=180^0\]\[Also,Sum \ of \ exterior \ angles \ of \ the \ \triangle=360^0 \] |dw:1357731900719:dw|

    • one year ago
  11. hba
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    \[\underline{2}:Any \ exterior \ a ngle \ is \ always \ equal \ t o \ supplement\ of \ its \ adjacent \ interior \ \angle\]\[e.g \ \angle d=180- \angle c\]

    • one year ago
  12. hba
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    \[\underline{3}:Exterior \ angles \ is \ always \ equal \ t o \ the \ s um \ of \ opposite \ interior \ angl e.\]\[e.g.<d=<a+<b\]

    • one year ago
  13. hba
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    \[\underline{4}:Sum \ of \ the \ measures \ of \ any \ two \ sides \ is \ always \ greater \ than \ the \ third \ side \] \[e.g.AB+BC>AC \\ or \ \ AC+BC>AB \]

    • one year ago
  14. hba
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    \[\underline{5}:Side \ opposite \ t o \ greater \ angl e \ is \ larger \ i n \ measure \ than \ that \ of \ smaller \ angl e.\]\[e.g. if \ i n \ ABC \ a>b \ BC>AB \ as \ BC \ opposite \ t o \ angl e \ a\]

    • one year ago
  15. hba
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    6:Altitude of a triangle is the perpendicular disrance from a vertex to opposite side.It may be inside,outside or on the triangle. Lemme show you what i am trying to say to you.|dw:1357734242316:dw|

    • one year ago
  16. hba
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    \[\underline{7}:AREA \ OF \ \triangle:\]\[Area=\frac{ 1 }{ 2 } \times Base \times height (Altitude)\]

    • one year ago
  17. hba
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    8:Perimeter:Sum of the sides of the triangle is called perimeter.

    • one year ago
  18. hba
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    \[\underline{TYPES \ OF \ \ TRIANGLE:}\]There are three types of triangles: a)Equilateral b)Isosceles c)Scalene

    • one year ago
  19. hba
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    Yeah, In Equilateral,All sides are equal In Isoscles,Any two side and In Scalene ,No side equal to other

    • one year ago
  20. hba
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    \[\Huge --- \text{END TO TRIANGLES}---\]

    • one year ago
  21. hba
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    \[\huge\ \underline{ RECTANGLE} :\]It is the most important quadrilateral.if in parallelogram all angles equal to 90 then it becomes rectangle.The larger side of rectangle is called length and shorter side as width.Also diagonal of rectangle are of equal length .i.e.AB=CD and BC=AD.

    • one year ago
  22. hba
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    |dw:1357735551081:dw| So, \[\huge\ Area=L \times W\] \[\huge\ Perimeter=2(L+W) \]

    • one year ago
  23. hba
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    \[\Huge --- \text{END TO RECTANGLE}---\]

    • one year ago
  24. hba
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    \[\huge\ \underline{SQUARE} :\]It is a rectangle with four sides which are equal. i.e. AB=BC=CD=DA If one side is x \[Area=x *x=x^2 \] Area of square can also be found by using diagonal d. \[Area=\frac{ d^2 }{ 2 } \] \[Perimeter \ of \ \square = 4x\] \[Diagonal=\sqrt{2} \times x\]

    • one year ago
  25. hba
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    |dw:1357736723318:dw|

    • one year ago
  26. hba
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    \[\Huge --- \text{END TO SQUARE}---\]

    • one year ago
  27. hba
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    \[\huge\ \underline{CIRCLE} :\]The set of points in a plane at the same distance from a certain fixed point is called a circle Um,the fixed point is called the centre of the circle and the distance from a point on circle to centre is called Radius.|dw:1357737289537:dw|

    • one year ago
  28. hba
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    CHORD:Line segment obtain by joining any two points on the circle e.g. DE DIAMETER:If a chord passes through the centre of the circle is called diameter. See in the fig:BC is marked as diameter Tangent: The line which touches only one point of the circle is called tangent.In above figure line m is tangent.

    • one year ago
  29. hba
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    CENTRAL ANGLE: An angle formed by two diff radii at centre is called central angle.In the figure <AOB is central angle.

    • one year ago
  30. hba
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    CIRCUMFERENCE:Boundary of a circle is called circumference.

    • one year ago
  31. hba
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    \[\huge\ C= \pi . d\] \[(As \ d=2r)\] \[\huge\ C=2 \pi r\]

    • one year ago
  32. hba
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    AREA OF CIRCLE: Area of circle is given by the formula. \[\huge\ A= \pi r^2\]

    • one year ago
  33. hba
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    \[\Huge{\color{red}{{THE Da \space END{\ddot{\smile}}}}}\]

    • one year ago
  34. phi
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    For definitions 5 and 6 under Angles you should spell out supplementary and complementary.

    • one year ago
  35. hba
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    Sorry dude.

    • one year ago
  36. Koikkara
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    hey, Really APPRECIATE you for the method of sharing Ideas...EXCELLENT JOB....HBA!!

    • one year ago
  37. hba
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    Thanks dude.

    • one year ago
  38. Koikkara
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    >>!!

    • one year ago
  39. hba
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    Thanks a lot :)

    • one year ago
  40. mikaela19900630
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    you did an amazing job hba

    • one year ago
  41. hba
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    Thank you :)

    • one year ago
  42. ashlynn143
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    that was very informative

    • one year ago
  43. hba
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    Thanks :)

    • one year ago
  44. joyflow
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    this will help a lot of people who are starting geometry

    • one year ago
  45. joyflow
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    good job by the way

    • one year ago
  46. hba
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    Well,I am gonna include the Heroen's formula in the next tutorial :) Because it is gonna be a lil huge :) Thanks a lot anyways :)

    • one year ago
  47. farukk
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    very useful keep it up.

    • one year ago
  48. hba
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    Thanks :)

    • one year ago
  49. Reaper534
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    guys i toght him that jk :D

    • one year ago
  50. hba
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    Haha lol :P

    • one year ago
  51. Reaper534
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    how long did tht take

    • one year ago
  52. hba
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    I don't know :P

    • one year ago
  53. farukk
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    @hba welcome:) or should i say my new teacher for mathematics?

    • one year ago
  54. Reaper534
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    i say 40min tops

    • one year ago
  55. hba
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    Yeah take it as 40 min :P @farukk Teacher lol,Ham tau aap kai bhai hai :D

    • one year ago
  56. farukk
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    hahaha tu kia hoa math bato se hi seekhi jati ha :p

    • one year ago
  57. Reaper534
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    ?????

    • one year ago
  58. hba
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    @farukk Msg me if you need help .

    • one year ago
  59. amoodarya
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    tnx Please comment on my activity

    • one year ago
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  60. farukk
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    yeah it's informative:)

    • one year ago
  61. UnkleRhaukus
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    great work @hba

    • one year ago
  62. hba
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    Thank you very much. I am really sorry for not putting the heroen's formula though.

    • one year ago
  63. syhna
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    nice work :D

    • one year ago
  64. hba
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    Thanks :)

    • one year ago
  65. Reaper534
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    yeah i toght him well XD

    • one year ago
  66. syhna
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    reaper534_ nice joke :D aha peace XD

    • one year ago
  67. hba
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    Lol learn to spell first then teach others :P

    • one year ago
  68. Reaper534
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    hahahahah :D it ain english class

    • one year ago
  69. Reaper534
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    @hba bump it

    • one year ago
  70. abb0t
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    How did you know I don't know Geometry o.0? n e wayz, bookmarked. great review!

    • one year ago
  71. hba
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    Thanks :P

    • one year ago
  72. hba
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    I just shared it with you :)

    • one year ago
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