My tutorial on plane geometry.

- hba

My tutorial on plane geometry.

- chestercat

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- 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 \

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- hba

\[TYPES \ OF \ ANGLES:\]|dw:1357729201753:dw|

- 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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## More answers

- hba

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

- 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

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

- hba

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

- hba

\[\Huge --- \text{END TO ANGLES}---\]

- hba

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

- 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

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

- hba

\[\underline{3}:Exterior \ angles \ is \ always \ equal \ t o \ the \ s um \ of \ opposite \ interior \ angl e.\]\[e.g.

- 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

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

- hba

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

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

- hba

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

- hba

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

- hba

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

- hba

\[\Huge --- \text{END TO TRIANGLES}---\]

- 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

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

- hba

\[\Huge --- \text{END TO RECTANGLE}---\]

- 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

|dw:1357736723318:dw|

- hba

\[\Huge --- \text{END TO SQUARE}---\]

- 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

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

CENTRAL ANGLE: An angle formed by two diff radii at centre is called central angle.In the figure

- hba

CIRCUMFERENCE:Boundary of a circle is called circumference.

- hba

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

- hba

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

- hba

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

- phi

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

- hba

Sorry dude.

- Koikkara

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

- hba

Thanks dude.

- Koikkara

>>!!

- hba

Thanks a lot :)

- anonymous

you did an amazing job hba

- hba

Thank you :)

- anonymous

that was very informative

- hba

Thanks :)

- anonymous

this will help a lot of people who are starting geometry

- anonymous

good job by the way

- 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

very useful keep it up.

- hba

Thanks :)

- anonymous

guys i toght him that jk :D

- hba

Haha lol :P

- anonymous

how long did tht take

- hba

I don't know :P

- anonymous

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

- anonymous

i say 40min tops

- hba

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

- anonymous

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

- anonymous

?????

- hba

@farukk Msg me if you need help .

- amoodarya

tnx
Please comment on my activity

##### 1 Attachment

- anonymous

yeah it's informative:)

- UnkleRhaukus

great work @hba

- hba

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

- anonymous

nice work :D

- hba

Thanks :)

- anonymous

yeah i toght him well XD

- anonymous

reaper534_ nice joke :D aha peace XD

- hba

Lol learn to spell first then teach others :P

- anonymous

hahahahah :D it ain english class

- anonymous

@hba bump it

- abb0t

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

- hba

Thanks :P

- hba

I just shared it with you :)

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