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Math: Triangles

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Re: Everything About Triangles For GMAT. [#permalink] New post 24 Nov 2009, 08:06
This will help a lot .. another thanks ..
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Re: Everything About Triangles For GMAT. [#permalink] New post 24 Nov 2009, 09:29
I wish somebody made a pdf compilation of Bunuel's posts... :shock: :shock:
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Re: Everything About Triangles For GMAT. [#permalink] New post 24 Nov 2009, 09:49
awesome guide thanks!
so there are other guides like this? I'm taking the GMAT tomorrow, I would love to have a quick but thorough review. can someone post the other guides? Thanks
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Re: Everything About Triangles For GMAT. [#permalink] New post 24 Nov 2009, 10:06
manifestdestiny wrote:
awesome guide thanks!
so there are other guides like this? I'm taking the GMAT tomorrow, I would love to have a quick but thorough review. can someone post the other guides? Thanks


Check out sticky threads in Math and Verbal forums. Pretty much everything important is collected up there.


and Good luck for tomorrow!
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Re: Everything About Triangles For GMAT. [#permalink] New post 24 Nov 2009, 14:48
+1

I would give +10 for this million dollar resources if it were allowed.

You wont find this much materials free of cost anywhere in the world.

You are highly resourceful. 8-)
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Re: Everything About Triangles For GMAT. [#permalink] New post 24 Nov 2009, 22:58
Thank you so much.
This is massive
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Re: Math: Triangles [#permalink] New post 08 Dec 2009, 15:33
Thank you for the awesome post..
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Re: Math: Triangles [#permalink] New post 27 Dec 2009, 06:04
Expert's post
logan wrote:
Exceptional... a really well compiled data on triangles and their properties...
the best part was to mention the problems from the official GMAT books.... +2

i think it would be worth mentioning the sine and cosine rules of triangles...

The law of sines (or Sine Rule):

If A, B and C are the angles made by the sides a= BC, b= CA & c= AB at the vertices of a triangle ABC, then according to the sine rule, (a/sin A) = (b/sin B) = (c/sin C)

The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known.

The law of cosines (or Cosine Rule) :

If A, B and C are the angles made by the sides a= BC, b= CA & c= AB at the vertices of a triangle ABC, then according to the cosine rule,

a^2 = b^2 + c^2 - 2bc(cos A); b^2 = a^2 + c^2 - 2ac(cos B); c^2 = a^2 + b^2 + 2ab(cos C)

The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known.


I withdrawn these rules as well as some other properties and formulas (there are plenty of them), as GMAT problems doesn't require knowing them for solving. No GMAT guide (as I know) mentions them in quant section.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Math: Triangles [#permalink] New post 11 Jan 2010, 20:07
KUDOS TO Gmat Club!!!!!!!!!!!!!!!!!!!! I think GMAT Club and my iphone are officially my new best friends and study buddies. :-D
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Re: Math: Triangles [#permalink] New post 12 Jan 2010, 16:43
Thanks a lot really good summary
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Re: Math: Triangles [#permalink] New post 13 Jan 2010, 18:03
Does the orthocenter = the centroid and if so, is it safe to say that altitudes=medians?
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Re: Math: Triangles [#permalink] New post 14 Jan 2010, 15:34
A masterpiece Bunuel . Amazing summary of triangle proprties. Some Questions to have more clarity .

Are the medians equal in length in a scalene traingle ?

Does the centroid neccasarily have to be a center of circumcircle of a scalene triangle or in other words, does it mean that each triangle can be circumcircled ?
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Re: Math: Triangles [#permalink] New post 14 Jan 2010, 16:01
Quote:
The SSA condition proves congruence if the angle is obtuse or right. In the case of the right angle (also known as the HL (Hypotenuse-Leg) condition or the RHS (Right-angle-Hypotenuse-Side) condition), we can calculate the third side and fall back on SSS.


For Obtuse angle also, above condition is true ?
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Re: Math: Triangles [#permalink] New post 14 Jan 2010, 16:16
Expert's post
gottabwise wrote:
Does the orthocenter = the centroid and if so, is it safe to say that altitudes=medians?


Generally orthocenter and centroid are not the same point. Generally altitude does not equal to median.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Math: Triangles [#permalink] New post 14 Jan 2010, 16:47
Expert's post
GMATMadeeasy wrote:
A masterpiece Bunuel . Amazing summary of triangle proprties. Some Questions to have more clarity .

Are the medians equal in length in a scalene traingle ?

Does the centroid neccasarily have to be a center of circumcircle of a scalene triangle or in other words, does it mean that each triangle can be circumcircled ?


Generally medians are not equal, so in scalene triangle medians are not equal.

Centroid is not the center of the circumscribed circle. (There was a typo in the text, edited.)

As for the circumscribed triangles: yes, any triangle can be circumscribed.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Everything About Triangles For GMAT. [#permalink] New post 04 Feb 2010, 14:39
GMAT TIGER wrote:
+1

I would give +10 for this million dollar resources if it were allowed.

You wont find this much materials free of cost anywhere in the world.

You are highly resourceful. 8-)


That's Perfect giving..!

Great resource.. which I cud realize in no time... just with in 1 hr of browsing this site...
Looking forwards to get overwhelmed..
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Re: Math: Triangles [#permalink] New post 15 Feb 2010, 00:01
excellent post! thanks a lot Bunuel!
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Re: Math: Triangles [#permalink] New post 14 Mar 2010, 01:20
Bunuel,
First of all thank you for the excellent compilation. I am using MGMAT books. And on this page I found many triangle concepts not covered in the book. Scary actually.

I wud like to know from other knowledgeable members, what they think about MGMAT books in terms of coverage of concepts?
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Re: Math: Triangles [#permalink] New post 05 Jun 2010, 05:05
thanks! this is really helpful!
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Re: Math: Triangles [#permalink] New post 17 Jun 2010, 11:06
Quote:
Usually called "half of base times height", the area of a triangle is given by the formula below.
• A=\frac{hb}{2}

Other formula:
• A=\frac{P*r}{2}

• A=\frac{abc}{4R}

Where b is the length of the base, a and c the other sides; h is the length of the corresponding altitude; R is the Radius of circumscribed circle; r is the radius of inscribed circle; P is the perimeter


Just to clarify, is P the perimeter of the circle or the triangle?
Quote:
• For an isosceles triangle with given length of equal sides right triangle (included angle) has the largest area.


Will u elaborate on this please? I'm not sure how this works.

Thanks a lot of the summary, very complete and succinct! :D
Re: Math: Triangles   [#permalink] 17 Jun 2010, 11:06
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