## hba 2 years ago My tutorial on plane geometry.

1. hba

$\Huge{\color{gold}{\star \star \star}\color{red}{\text{Plane Geometry}}}$ $\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|

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$TYPES \ OF \ ANGLES:$|dw:1357729201753:dw|

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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|

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$\underline {2}:Sum \ of \ all \ angles \ about \ a \ point \ is \ 360 ^0$|dw:1357729894167:dw|

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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

$\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.$

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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|

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$\Huge --- \text{END TO ANGLES}---$

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$\underline{TRIANGLE}:A \ closed \ figure \ with \ three \ angles \ and \ three \ straight \ sides$$is \ called \ a \ \triangle.$

10. hba

$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

$\underline{2}:Any \ exterior \ a ngle \ is \ always \ equal \ t o \ supplement\ of \ its \ adjacent \ interior \ \angle$$e.g \ \angle d=180- \angle c$

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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$

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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

$\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

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|

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$\underline{7}:AREA \ OF \ \triangle:$$Area=\frac{ 1 }{ 2 } \times Base \times height (Altitude)$

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8:Perimeter:Sum of the sides of the triangle is called perimeter.

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$\underline{TYPES \ OF \ \ TRIANGLE:}$There are three types of triangles: a)Equilateral b)Isosceles c)Scalene

19. hba

Yeah, In Equilateral,All sides are equal In Isoscles,Any two side and In Scalene ,No side equal to other

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$\Huge --- \text{END TO TRIANGLES}---$

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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.

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|dw:1357735551081:dw| So, $\huge\ Area=L \times W$ $\huge\ Perimeter=2(L+W)$

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$\Huge --- \text{END TO RECTANGLE}---$

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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. $Area=\frac{ d^2 }{ 2 }$ $Perimeter \ of \ \square = 4x$ $Diagonal=\sqrt{2} \times x$

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|dw:1357736723318:dw|

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$\Huge --- \text{END TO SQUARE}---$

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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|

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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.

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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.

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CIRCUMFERENCE:Boundary of a circle is called circumference.

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$\huge\ C= \pi . d$ $(As \ d=2r)$ $\huge\ C=2 \pi r$

32. hba

AREA OF CIRCLE: Area of circle is given by the formula. $\huge\ A= \pi r^2$

33. hba

$\Huge{\color{red}{{THE Da \space END{\ddot{\smile}}}}}$

34. phi

For definitions 5 and 6 under Angles you should spell out supplementary and complementary.

35. hba

Sorry dude.

36. Koikkara

hey, Really APPRECIATE you for the method of sharing Ideas...EXCELLENT JOB....HBA!!

37. hba

Thanks dude.

38. Koikkara

>>!!

39. hba

Thanks a lot :)

40. mikaela19900630

you did an amazing job hba

41. hba

Thank you :)

42. ashlynn143

that was very informative

43. hba

Thanks :)

44. joyflow

this will help a lot of people who are starting geometry

45. joyflow

good job by the way

46. hba

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

very useful keep it up.

48. hba

Thanks :)

49. Reaper534

guys i toght him that jk :D

50. hba

Haha lol :P

51. Reaper534

how long did tht take

52. hba

I don't know :P

53. farukk

@hba welcome:) or should i say my new teacher for mathematics?

54. Reaper534

i say 40min tops

55. hba

Yeah take it as 40 min :P @farukk Teacher lol,Ham tau aap kai bhai hai :D

56. farukk

hahaha tu kia hoa math bato se hi seekhi jati ha :p

57. Reaper534

?????

58. hba

@farukk Msg me if you need help .

59. amoodarya

tnx Please comment on my activity

60. farukk

yeah it's informative:)

61. UnkleRhaukus

great work @hba

62. hba

Thank you very much. I am really sorry for not putting the heroen's formula though.

63. syhna

nice work :D

64. hba

Thanks :)

65. Reaper534

yeah i toght him well XD

66. syhna

reaper534_ nice joke :D aha peace XD

67. hba

Lol learn to spell first then teach others :P

68. Reaper534

hahahahah :D it ain english class

69. Reaper534

@hba bump it

70. abb0t

How did you know I don't know Geometry o.0? n e wayz, bookmarked. great review!

71. hba

Thanks :P

72. hba

I just shared it with you :)