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hba

  • one year ago

My tutorial on plane geometry.

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  1. hba
    • one year ago
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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|

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

  3. hba
    • one year ago
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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|

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

  5. hba
    • one year ago
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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|

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

  7. hba
    • one year ago
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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|

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

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

  10. hba
    • one year ago
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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|

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

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

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

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

  15. hba
    • one year ago
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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|

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

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

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

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

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

  21. hba
    • one year ago
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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.

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

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

  24. hba
    • one year ago
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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. \[Area=\frac{ d^2 }{ 2 } \] \[Perimeter \ of \ \square = 4x\] \[Diagonal=\sqrt{2} \times x\]

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

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

  27. hba
    • one year ago
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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|

  28. hba
    • one year ago
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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.

  29. hba
    • one year ago
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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.

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

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

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

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

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

  35. hba
    • one year ago
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    Sorry dude.

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

  37. hba
    • one year ago
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    Thanks dude.

  38. Koikkara
    • one year ago
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    >>!!

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

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

  41. hba
    • one year ago
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    Thank you :)

  42. ashlynn143
    • one year ago
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    that was very informative

  43. hba
    • one year ago
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    Thanks :)

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

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

  46. hba
    • one year ago
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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 :)

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

  48. hba
    • one year ago
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    Thanks :)

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

  50. hba
    • one year ago
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    Haha lol :P

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

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

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

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

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

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

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

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

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

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

  61. UnkleRhaukus
    • one year ago
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    great work @hba

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

  63. syhna
    • one year ago
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    nice work :D

  64. hba
    • one year ago
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    Thanks :)

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

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

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

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

  69. Reaper534
    • one year ago
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    @hba bump it

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

  71. hba
    • one year ago
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    Thanks :P

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

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