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hba

  • 2 years ago

My tutorial on plane geometry.

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  1. hba
    • 2 years 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
    • 2 years ago
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    \[TYPES \ OF \ ANGLES:\]|dw:1357729201753:dw|

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

  5. hba
    • 2 years 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
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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
    • 2 years 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
    • 2 years ago
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    \[\Huge --- \text{END TO ANGLES}---\]

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

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

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

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

  19. hba
    • 2 years 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
    • 2 years ago
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    \[\Huge --- \text{END TO TRIANGLES}---\]

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

  23. hba
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    \[\Huge --- \text{END TO RECTANGLE}---\]

  24. hba
    • 2 years 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
    • 2 years ago
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    |dw:1357736723318:dw|

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

  27. hba
    • 2 years 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
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    CIRCUMFERENCE:Boundary of a circle is called circumference.

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

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

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

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

  35. hba
    • 2 years ago
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    Sorry dude.

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

  37. hba
    • 2 years ago
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    Thanks dude.

  38. Koikkara
    • 2 years ago
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    >>!!

  39. hba
    • 2 years ago
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    Thanks a lot :)

  40. mikaela19900630
    • 2 years ago
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    you did an amazing job hba

  41. hba
    • 2 years ago
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    Thank you :)

  42. ashlynn143
    • 2 years ago
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    that was very informative

  43. hba
    • 2 years ago
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    Thanks :)

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

  45. joyflow
    • 2 years ago
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    good job by the way

  46. hba
    • 2 years 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
    • 2 years ago
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    very useful keep it up.

  48. hba
    • 2 years ago
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    Thanks :)

  49. Reaper534
    • 2 years ago
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    guys i toght him that jk :D

  50. hba
    • 2 years ago
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    Haha lol :P

  51. Reaper534
    • 2 years ago
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    how long did tht take

  52. hba
    • 2 years ago
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    I don't know :P

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

  54. Reaper534
    • 2 years ago
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    i say 40min tops

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

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

  57. Reaper534
    • 2 years ago
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    ?????

  58. hba
    • 2 years ago
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    @farukk Msg me if you need help .

  59. amoodarya
    • 2 years ago
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    tnx Please comment on my activity

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  60. farukk
    • 2 years ago
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    yeah it's informative:)

  61. UnkleRhaukus
    • 2 years ago
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    great work @hba

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

  63. syhna
    • 2 years ago
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    nice work :D

  64. hba
    • 2 years ago
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    Thanks :)

  65. Reaper534
    • 2 years ago
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    yeah i toght him well XD

  66. syhna
    • 2 years ago
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    reaper534_ nice joke :D aha peace XD

  67. hba
    • 2 years ago
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    Lol learn to spell first then teach others :P

  68. Reaper534
    • 2 years ago
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    hahahahah :D it ain english class

  69. Reaper534
    • 2 years ago
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    @hba bump it

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

  71. hba
    • 2 years ago
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    Thanks :P

  72. hba
    • 2 years ago
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    I just shared it with you :)

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