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Properties of Triangles
by Total Gadha - Thursday, 5 July 2007, 06:40 AM
 

cat 2007 cat 2008 xat 2008 mba 2008 properties of trianglesIt would be a shame if CAT 2007 or CAT 2008 aspirants have still not discovered that geometry is one of the most important areas to prepare in the quant section. They should also know that triangle is the most common figure they will see in the geometry section. Be it a quadrilateral or a hexagon, triangles and their properties will be present in every figure. Although the ideal way to learn these properties is to practice and derive all the theorems related to these properties themselves, the students can go through this small compendium to have a quick recap of those formula. The following properties do not cover the similarity of triangles. Of course that will take an entire article by itself.


cat 2007 cat 2008 xat 2008 properties of triangles

In the next chapter, I will cover similarity of triangles and its uses.

Total Gadha

I am afraid I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week.

 

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Re: Properties of Triangles
by Gul Gul - Thursday, 5 July 2007, 10:29 AM
 

AWESOME...!!!!!

Waiting for Circles........I know they will be here..smile

Thanks Genius...

Gullz

Re: Properties of Triangles
by clenched fist - Thursday, 5 July 2007, 11:18 AM
  Simply brilliant!!

I'm really hoping that you would complete such fundu articles before end of July for us CAT 07 aspirants so that we can apply whatever gaps that have been filled through such articles in the sums that we would solve in the mock CATs smile

CF
Re: Properties of Triangles
by srini vasan - Thursday, 5 July 2007, 11:23 AM
  Thanks TG.
One Correction -  Angle (BIC) = 90 + (A/2) in point 7 

-Srini
Re: Properties of Triangles
by rhishabh garg - Thursday, 5 July 2007, 11:56 AM
 

gud work TG.....

i think it is the appolonius theorem and the internal bisector theorem which are used most of the times..

rhishabh

Re: Properties of Triangles
by Kunal Gupta - Thursday, 5 July 2007, 12:51 PM
 

Hi TG,

Pls start a thread for this kinda Q and start with the less complex probs so that we can absorbe the fundas be4 solving Geo section probs given by u...

Article is awesome no doubt abt that!!

Waiting 4 ur action..

Re: Properties of Triangles
by Sujeet Shrivastava - Thursday, 5 July 2007, 01:13 PM
 

Hi,

Awesome article.  You are the best teacher I have ever come across.  The way you explain things is awesome.  Nobody can explain better than this.

Waiting for your next article of Geometry...

Regards,

Sujeet S.

 

Re: Properties of Triangles
by karan maheshwari - Thursday, 5 July 2007, 02:08 PM
 

hi tg  thanks....

 it's nice need more topics on triangles

Re: Properties of Triangles
by Shyamali Saxena - Thursday, 5 July 2007, 03:44 PM
 

Hi TG

Your summation of all thoughts on triangles shall be a great help. Thank you.

I've been solving the questions on geometry in TG Quiz section.

Could you advice upon where we can get solutions for these?

I'm not able to solve a few.

Thanks

SHYAMALI

Re: Properties of Triangles
by prafull kumar - Thursday, 5 July 2007, 08:10 PM
 

Thnx TG ,in tons .

u hv rally made me belive that i can do good in quant.I can better say this site has turned my preparation towards right direction.u nd ur team is best .nd haan  i am proud to be a part of GADHA family.big grinsmileapprove

Re: Properties of Triangles
by Kumar Kislay - Thursday, 5 July 2007, 09:56 PM
  Great Stuff....Thanks TG....smile

Waiting 4 Similarity of triangles....
Re: Properties of Triangles
by abhinav sharma - Friday, 6 July 2007, 05:54 PM
 

Dear TG,

i want to take printout of the lessons you paste.

But i doesnt come out complete.

please suggest me how to take full print of lessons.

thanks n regards

abhi

Re: Properties of Triangles
by Total Gadha - Saturday, 7 July 2007, 12:46 PM
  Hi Gullz,

Yes, they will be here any time soon. smile

Total Gadha
Re: Properties of Triangles
by Total Gadha - Saturday, 7 July 2007, 12:48 PM
  Hi CF,

I also hope that I shall be able to finish the chapters before July. Unfortunately, the peak teaching season has arrived and I'm taking classes everyday. sad Trying my best to finish chapters.

Total Gadha
Re: Properties of Triangles
by Total Gadha - Saturday, 7 July 2007, 12:51 PM
  Thanks Rishabh smile
Re: Properties of Triangles
by Total Gadha - Saturday, 7 July 2007, 12:52 PM
  Hi Srini,

Corrected. smile

Total Gadha
Re: Properties of Triangles
by Deep Thinker Gadha - Sunday, 8 July 2007, 12:47 PM
  smile smile smile
Re: Properties of Triangles
by ashish tyagi - Sunday, 8 July 2007, 08:12 PM
 

really  great work tg ,

i feel lot of problem in geometry but if u will do such type of work in future then i'm feeling that i can crack the cat , pls give some more example n how can we use these theorem in questions.........thnx a lot............... kiss

Re: Properties of Triangles
by Amishe 800 - Monday, 9 July 2007, 09:50 AM
 

appreciated !!! ...awesome way to present things ....

waiting for upcoming chapters from you ...

Re: Properties of Triangles
by sorabh Vij - Monday, 9 July 2007, 11:47 AM
  hey,next time can u plz put a more printer frrinedly page..i would b extremely greatful to u and so will b many oders..
Re: Properties of Triangles
by Gkchamp Champ - Monday, 9 July 2007, 03:43 PM
 

The Article is really cool .....But got some doubts .....

I woulb be graetful if you could provide answers .

1. Does the Apollinous theorem applicable for Triangles with medians or its for Triangle in general.

Same is the case for Internal Bisector Theorem ...

Re: Properties of Triangles
by tripti pathak - Monday, 9 July 2007, 07:48 PM
 

The article is much better than my  coaching class stuff

thanks TG

Re: Properties of Triangles
by Total Gadha - Tuesday, 10 July 2007, 12:15 AM
  Hi Ashish,

If you promise to try your best to crack the CAT, I promise to work hard at my articles. smile

Thanks for the praise btw, it pushes me to do better and better. smile

Total Gadha
Re: Properties of Triangles
by Total Gadha - Tuesday, 10 July 2007, 12:17 AM
  Hi Gkchamp,

The Apollonius theorem is valid for medians, in any triangle. So is internal bisector theorem.

Total Gadha
Re: Properties of Triangles
by Total Gadha - Tuesday, 10 July 2007, 12:17 AM
  Thanks Tripti smile
Re: Properties of Triangles
by Anubhav Jain - Tuesday, 10 July 2007, 05:41 PM
 

hey TG

simply Great work!!! appreciate your efforts. We hope mensuration is soon coming up, your articles are of great helpsmilewink.

Re: Properties of Triangles
by sorabh Vij - Wednesday, 11 July 2007, 12:19 AM
 

Hey,i cannot view the formulas and tricks put in the image form in this page...i had viewed them before but now i am not able to do the same..its just not displayin on the screen...Hv u removed it..??? dat seems unlikely...

Plz HELP
Re: Properties of Triangles
by Total Gadha - Wednesday, 11 July 2007, 01:20 AM
  I can view them, there's nothing wrong here. Have you changed the settings of your browser?
Re: Properties of Triangles
by abc abc - Wednesday, 11 July 2007, 11:48 AM
 

Hi,

In the problem after ponit 9 ( Line Joining the Mid points);

How do I get E and D to be the mid-points of sides AB and AC respectively?

Didnt get this. Please explain.

Thanks,

Meenakshi.

Re: Properties of Triangles
by sakshi Gupta - Wednesday, 11 July 2007, 06:46 PM
 

hi TG

in the problem of line joining the mid point how can we say that E and D are also the midpoints of AB and AC resp. how can we find out the area of other triangles on the basis of the first one?

Please tell again

Thanks

Re: Properties of Triangles
by Total Gadha - Wednesday, 11 July 2007, 11:21 PM
  Hi Meenakshi and Sakshi,

In triangle AED, GF // ED and passing through one of the midpoints G.Therefore, it passes through the other midpoint also. Therefore, F is also a midpoint. Apply the same principle in triangle ABD (EF // BD) and find E as midoint, and so on.

Total Gadha
Re: Properties of Triangles
by Mohit Goyal - Thursday, 12 July 2007, 11:21 AM
  Hi TG,

Its my 1st post to TG.com....Great article for Triangles at glance and very nice way of putting up minute detatils.Thanks  TG, articles are really of great help.

look4mady
Re: Properties of Triangles
by Namrata Kher - Friday, 13 July 2007, 05:16 PM
  Hi TG!
this is awesome!
its better than all coaching centre material. it has made me confident in triangles now.
waiting for some fore great articles like this
thanks
namrata...
Re: Properties of Triangles
by Puneet Kabra - Tuesday, 24 July 2007, 02:21 PM
 

Dear Mr. TG

I have come across "Exterior Angle Bisector Thm"

But i didnt understand the relation...Can u pls help me in this?

Thx in advance.

Puneet

Re: Properties of Triangles
by Srikanth Gadige - Monday, 13 August 2007, 02:39 PM
  Hi ,
What is appolonius theorem ?? can you explain??
-srikanth.
Re: Properties of Triangles
by Puneet Kabra - Friday, 17 August 2007, 04:01 PM
 

I was able to derive it...

Thx

Re: Properties of Triangles
by Amit Raj - Thursday, 27 December 2007, 10:24 AM
 

TG Sir,

Great Article..

Please teach us about Circles.

Waiting for that.

Amit..

Re: Properties of Triangles
by najeeb ahmed - Saturday, 2 February 2008, 11:30 AM
  wooo... I'm short of words.. they way you explain things is brilliant... Keep going...
Re: Properties of Triangles
by sanjeev ganesh - Saturday, 9 August 2008, 08:29 AM
 

Hi,

I have got a prob on RECTANGLE:

Let the sides of the rectangle be a & b. If opposite vertex are joined, then the length of the line obtained joining them will be equal to the longest side of the rectangle. Next, diagonal bisects new line into 2 equal halves. Hence what is the ratios of lengths of the rectangle.

Plz let me know the method in solving the problem.

 

Cheers,

Sanjeev

 

Re: Properties of Triangles
by sanjeev ganesh - Saturday, 9 August 2008, 08:29 AM
 

Hi,

I have got a prob on RECTANGLE:

Let the sides of the rectangle be a & b. If opposite vertex are joined, then the length of the line obtained joining them will be equal to the longest side of the rectangle. Next, diagonal bisects new line into 2 equal halves. Hence what is the ratios of lengths of the rectangle.

Plz let me know the method in solving the problem.

 

Cheers,

Sanjeev

 

Re: Properties of Triangles
by sanjeev ganesh - Saturday, 9 August 2008, 08:31 AM
 

Hi,

I have got a prob on RECTANGLE:

Let the sides of the rectangle be a & b. If opposite vertex are joined, then the length of the line obtained joining them will be equal to the longest side of the rectangle. Next, diagonal bisects new line into 2 equal halves. Hence what is the ratios of lengths of the rectangle.

Plz let me know the method in solving the problem.

 

Cheers,

Sanjeev

Re: Properties of Triangles
by sanjeev ganesh - Saturday, 9 August 2008, 08:49 AM
 

Hi,

Forum, is pretty awesome and informative in brushing my school days.

Can you please help me on a Rectangle probl:

Let sides of a rectangle be a & b. If opposite vertex are joined, then the length of the line obtained joining them will be equal to the longest side of the rectangle. Next, diagonal bisects new line into 2 equal halves. Hence what will be rectangle side ratio.

Plz let me know the method in solving the problem.

 

Cheers,

Sanjeev

Re: Properties of Triangles
by Aashish Dua - Friday, 29 August 2008, 07:05 PM
 

Hie TG Sir,

You have summed up the concepts of 8th, 9th and 10th pretty nicely.

Thanks

Regards

Re: Properties of Triangles
by manish singh - Tuesday, 23 September 2008, 10:59 PM
  hi, i have finished my fundamental exercises on triangle but still i am not able to solve questions on CAT pattern assist me soon
Re: Properties of Triangles
by manoj singh - Thursday, 4 June 2009, 03:04 AM
  TG
I didnt understand how in ratio of triangle to trapezium problem how E will be the mid point AB plz reply.
Re: Properties of Triangles
by aditya ranjan - Wednesday, 17 June 2009, 01:42 AM
  awsome article really loved
can u post article on circles plzzzzzzzzzzzzzzzzzzz
Re: Properties of Triangles
by aviral srivastava - Thursday, 9 July 2009, 02:36 PM
 

problem (cat 2003)---

it says dat AD=CD=BC

DIS MEANS DAT ANGLES-DAC=ABC=ACD=x

ANGLE  ACB=180-96=84

ACCORDING TO properties of triangle---angles---acb+abc+bac=180

84+2x=180

2x=96

x=48

hence angle DBC=84-48=36(Ans)

Re: Properties of Triangles
by Viraj Bhise - Friday, 10 July 2009, 11:33 AM
 

Great article.... Awesome...

Thanks TG..

Re: Properties of Triangles
by swati saxena - Saturday, 11 July 2009, 11:37 PM
 

My geometry has been really weak.. these notes are extremely helpful!

i have given the geom quiz also but there were many ques i could'nt crack.. can we please have the solutions for the quiz soon

also can we have more such noted on other geometry figures

 

thanks 

 

@tg
by mohit budhiraja - Sunday, 26 July 2009, 01:22 AM
  visiting this site made me realize why i scored a ittle less in quants in cat '08 where i cud have very easily scored 57-60 and got all calls...neverthless,u are doin a wonderful job and i have the guidance that was missing durng '08 preparation....thanku tg 
Re: @tg
by Nakul Kothari - Thursday, 30 July 2009, 01:05 AM
  awesome article.....after reading it i could solve much more problems ....thanks tg....now i will become the insane gadha of this site!!!!smile
Re: @tg
by bhupi suhag - Friday, 21 August 2009, 04:36 PM
  what is the distance between the centres of the largest of the circle and the smallest circle that are drawn touching all the three sides of the equilateral triangle of the side 30cm.....pls solve
Re: Properties of Triangles
by hbk Not joining IIML - Sunday, 6 September 2009, 12:39 PM
  Hi TG
In the 3rd point of the 4th property do u mean that AD = x ?
Re: Properties of Triangles
by neha jirafe - Wednesday, 11 November 2009, 12:22 AM
  Hi TG,
Thanks for the awesome article,

Can you please tell me how do we find the area of largest rectangle/square that can be inscribed in a Right angled triangle/ or any other triangle.

Thanks in advance for the reply
Re: Properties of Triangles
by sim card - Wednesday, 11 November 2009, 01:45 PM
 

Its a great article, why didn't I come across it earlier. 

Re: Properties of Triangles
by kanika arora - Saturday, 21 November 2009, 02:24 PM
  ABCD is a trapezium with sides AB and CD parallel to each other with CD = 4 cm and AB = 10 cm, a point E is taken on the side AB such that AE = 4 cm. Another point F is chosen on CD such that the are of the triangle AEF = 12 sq. cm. If BC = 10 cm and AC = 2√13, then find the area of the quadrilateral AECD.

  a12 sq. cm
  b6 sq. cm
  c24 sq. cm
  d48 sq. cm
  eNone of these

Regards
Kanika
answer
by sanket t - Saturday, 21 November 2009, 07:09 PM
  24

Re: Properties of Triangles
by Ankit Garg - Sunday, 29 November 2009, 01:20 AM
  that's not possible in rectangle ... a diagonal can never be equal to the longest side ...
Re: Properties of Triangles
by tapas mani shyam - Sunday, 29 November 2009, 11:43 PM
  agresmileed with sanket..its 24
Re: Properties of Triangles
by xlr pmir - Wednesday, 28 April 2010, 08:58 PM
  copied frm tg e booktongueout
Re: Properties of Triangles
by siddharth jain - Friday, 3 September 2010, 04:53 PM
  hey bro... can u send tg e book of geometry to me,,,
plz it would be a great help...
my id,.... siddharth.jain_88@in.com
Re: Properties of Triangles
by siddharth jain - Friday, 3 September 2010, 04:54 PM
   sir,,,,
 plz give some material and shortcuts in geometry
Re: Properties of Triangles
by saurabh tibrewal - Monday, 20 September 2010, 02:32 AM
  thats a mistake... assume AE=EB
Re: Properties of Triangles
by arun kumar - Wednesday, 6 October 2010, 01:14 PM
 

kanika....pls explain the answer...i have some confusion.......my ans..is 24...but i didnt use.....any data...

Re: Properties of Triangles
by KHUSHBOO SOLANKI - Wednesday, 13 October 2010, 07:48 PM
 

HI! THANK YOU SO MUCH  TO CLEAR THE BASIC CONCEPTS FOR TRIANGLES.  ITS A MUST READ ARTICLE.

PLEASE,PROVIDE FEW EXAMPLES ON THE SAME CONCEPT FOR PRACTICE.

Re: Properties of Triangles
by priya ravindran - Tuesday, 25 June 2013, 10:08 AM
  Tanks a lot............hopin formore articlessmile
Re: Properties of Triangles
by varun joshi - Thursday, 4 July 2013, 12:48 PM
 

been following you guys for years now.every year a new energy flows into mind while solving your problems.

cheerio

Re: Properties of Triangles
by Jeevraj Taralkar - Friday, 19 July 2013, 07:59 PM
  Hey Kanika & others,

Even I tried solving question but also checking the consistency of details as well.

Answer do come as 24 Sq. cm but BC=10 cm seems to be misleading

If AE=4 & distance between 2 parallel lines is 6 (from Area of triangle AEF = 12)
suppose perpendicular from pt C to AB is point X
Therefore, CX is the perpendicular distance between two parallel lines.


then AC2 = AX2 + CX2
[2(root 13)]2 = AX2 + 36
AX = 4

i.e. point E & X are same


but if BC = 10 and CE/CX = 6
then BX/BE should be 8

but AB = 10 =  AE + AB = 4 + 6
i.e. BE = 6

two different values for BE

Hope my comments are clear & am not confusing

Regret if I did!!!!!


Rgds
JT



Re: Properties of Triangles
by Jeevraj Taralkar - Friday, 19 July 2013, 08:07 PM
  Dear Sir,

this is about 1st properties of triangle mentioned above.

its cleared that sum of a two sides of a triangle is greater than 3rd side.

but our professor has also taught one more property based on this which I found as doubtful.

If a, b & c are sides of triangle, where c is greater side, then

For Right Angled Triangle:
c2 = a2 + b2

but: confusion is he also said
for obtuse angles triangle:
c2 > a2 + b2

& for acute angles triangle:
c2 < a2 + b2

I Just want to confirm, is it true always???



Re: @tg
by Jeevraj Taralkar - Friday, 19 July 2013, 08:16 PM
  Hi Bhupi,

I think, we can draw only one circle touching all the three sides of any triangle. There are no largest & smallest.

So distance should be zero.
Re: Properties of Triangles
by Jeevraj Taralkar - Friday, 19 July 2013, 08:18 PM
  Hey send it to me too, if u get it

my email ID is
jeevraj.vjti@gmail.com
Re: Properties of Triangles
by Jeevraj Taralkar - Sunday, 21 July 2013, 10:31 PM
  I dont find any reason to spoil the forum like this.

if U cant value add anything, stay away!!!!!!
Re: Properties of Triangles
by ankit SAHAY - Monday, 9 September 2013, 10:37 PM
  cant understand how to approach this question:

The sides of triangle ABC are a cm, b cm and c cm. The sides of triangle DEF are d cm, e cm and f cm. The following relations hold true.
a (a + b + c) = d2
b (a + b + c) = e2
c (a + b + c) = f2
Then triangle DEF is

pls respond