hba
  • hba
My tutorial on plane geometry.
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
hba
  • 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 \
hba
  • hba
\[TYPES \ OF \ ANGLES:\]|dw:1357729201753:dw|
hba
  • hba
\[PROPERTIES \ RELATED \ TO \ LINES \ AND \ ANGLES:\] \[\underline {1}:The \ \sum \ of \ measure \ of \ the \ angles \ at \ a \ point \ on \ one \ straight \ line \ is \ 180^0\] |dw:1357729712082:dw|

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hba
  • hba
\[\underline {2}:Sum \ of \ all \ angles \ about \ a \ point \ is \ 360 ^0 \]|dw:1357729894167:dw|
hba
  • hba
\[\underline{3}:Two \ lines \ l \ and \ m \ are \ perpendicular \ if \ they \ intersect \ at \ 90^0.We \ write \ this \ as \ l \ perp \ m \]|dw:1357730164742:dw|
hba
  • hba
\[\underline{4}:Shortest \ distance \ \between \ two \ lines \ or \ a \ point \ and \ a \ line \ is \ always \ perpendicular \ distance.\]\[\underline{5}: If \ the \ \sum \ of \ two \ angles \ is \ 180^0 \ they \ are \ called \ supp \ angles.\]\[\underline{6}:If \ the \sum of \ two \ angles \ is \ 90^0 \ they \ are \ called \ comp \ angles.\]
hba
  • hba
\[\underline{7}:If \ two \ lines \ intersect,opposite \ angles \ formed \ \ are \ called \ vertical \ \]\[angles \ and \ they \ are \ always \ equal. \] \[In \ figure \ : a=c \space and \ c=d\]|dw:1357730912103:dw|
hba
  • hba
\[\Huge --- \text{END TO ANGLES}---\]
hba
  • hba
\[\underline{TRIANGLE}:A \ closed \ figure \ with \ three \ angles \ and \ three \ straight \ sides\]\[is \ called \ a \ \triangle.\]
hba
  • 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|
hba
  • hba
\[\underline{2}:Any \ exterior \ a ngle \ is \ always \ equal \ t o \ supplement\ of \ its \ adjacent \ interior \ \angle\]\[e.g \ \angle d=180- \angle c\]
hba
  • hba
\[\underline{3}:Exterior \ angles \ is \ always \ equal \ t o \ the \ s um \ of \ opposite \ interior \ angl e.\]\[e.g.
hba
  • hba
\[\underline{4}:Sum \ of \ the \ measures \ of \ any \ two \ sides \ is \ always \ greater \ than \ the \ third \ side \] \[e.g.AB+BC>AC \\ or \ \ AC+BC>AB \]
hba
  • hba
\[\underline{5}:Side \ opposite \ t o \ greater \ angl e \ is \ larger \ i n \ measure \ than \ that \ of \ smaller \ angl e.\]\[e.g. if \ i n \ ABC \ a>b \ BC>AB \ as \ BC \ opposite \ t o \ angl e \ a\]
hba
  • 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|
hba
  • hba
\[\underline{7}:AREA \ OF \ \triangle:\]\[Area=\frac{ 1 }{ 2 } \times Base \times height (Altitude)\]
hba
  • hba
8:Perimeter:Sum of the sides of the triangle is called perimeter.
hba
  • hba
\[\underline{TYPES \ OF \ \ TRIANGLE:}\]There are three types of triangles: a)Equilateral b)Isosceles c)Scalene
hba
  • hba
Yeah, In Equilateral,All sides are equal In Isoscles,Any two side and In Scalene ,No side equal to other
hba
  • hba
\[\Huge --- \text{END TO TRIANGLES}---\]
hba
  • hba
\[\huge\ \underline{ RECTANGLE} :\]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.
hba
  • hba
|dw:1357735551081:dw| So, \[\huge\ Area=L \times W\] \[\huge\ Perimeter=2(L+W) \]
hba
  • hba
\[\Huge --- \text{END TO RECTANGLE}---\]
hba
  • hba
\[\huge\ \underline{SQUARE} :\]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. \[Area=\frac{ d^2 }{ 2 } \] \[Perimeter \ of \ \square = 4x\] \[Diagonal=\sqrt{2} \times x\]
hba
  • hba
|dw:1357736723318:dw|
hba
  • hba
\[\Huge --- \text{END TO SQUARE}---\]
hba
  • hba
\[\huge\ \underline{CIRCLE} :\]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|
hba
  • hba
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.
hba
  • hba
CENTRAL ANGLE: An angle formed by two diff radii at centre is called central angle.In the figure
hba
  • hba
CIRCUMFERENCE:Boundary of a circle is called circumference.
hba
  • hba
\[\huge\ C= \pi . d\] \[(As \ d=2r)\] \[\huge\ C=2 \pi r\]
hba
  • hba
AREA OF CIRCLE: Area of circle is given by the formula. \[\huge\ A= \pi r^2\]
hba
  • hba
\[\Huge{\color{red}{{THE Da \space END{\ddot{\smile}}}}}\]
phi
  • phi
For definitions 5 and 6 under Angles you should spell out supplementary and complementary.
hba
  • hba
Sorry dude.
Koikkara
  • Koikkara
hey, Really APPRECIATE you for the method of sharing Ideas...EXCELLENT JOB....HBA!!
hba
  • hba
Thanks dude.
Koikkara
  • Koikkara
>>!!
hba
  • hba
Thanks a lot :)
anonymous
  • anonymous
you did an amazing job hba
hba
  • hba
Thank you :)
anonymous
  • anonymous
that was very informative
hba
  • hba
Thanks :)
anonymous
  • anonymous
this will help a lot of people who are starting geometry
anonymous
  • anonymous
good job by the way
hba
  • 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 :)
anonymous
  • anonymous
very useful keep it up.
hba
  • hba
Thanks :)
anonymous
  • anonymous
guys i toght him that jk :D
hba
  • hba
Haha lol :P
anonymous
  • anonymous
how long did tht take
hba
  • hba
I don't know :P
anonymous
  • anonymous
@hba welcome:) or should i say my new teacher for mathematics?
anonymous
  • anonymous
i say 40min tops
hba
  • hba
Yeah take it as 40 min :P @farukk Teacher lol,Ham tau aap kai bhai hai :D
anonymous
  • anonymous
hahaha tu kia hoa math bato se hi seekhi jati ha :p
anonymous
  • anonymous
?????
hba
  • hba
@farukk Msg me if you need help .
amoodarya
  • amoodarya
tnx Please comment on my activity
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anonymous
  • anonymous
yeah it's informative:)
UnkleRhaukus
  • UnkleRhaukus
great work @hba
hba
  • hba
Thank you very much. I am really sorry for not putting the heroen's formula though.
anonymous
  • anonymous
nice work :D
hba
  • hba
Thanks :)
anonymous
  • anonymous
yeah i toght him well XD
anonymous
  • anonymous
reaper534_ nice joke :D aha peace XD
hba
  • hba
Lol learn to spell first then teach others :P
anonymous
  • anonymous
hahahahah :D it ain english class
anonymous
  • anonymous
@hba bump it
abb0t
  • abb0t
How did you know I don't know Geometry o.0? n e wayz, bookmarked. great review!
hba
  • hba
Thanks :P
hba
  • hba
I just shared it with you :)

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