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Math: Triangles

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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, 05:51
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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.
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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!!!;

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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
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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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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
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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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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
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Re: Math: Triangles [#permalink] New post 18 Jun 2010, 01:14
Expert's post
bely202 wrote:
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


1. P is the perimeter of the triangle.
2. For instance if we have an isosceles triangle with equal sides of 1, the area will be greatest when it is a right angled triangle (max area in this case would be 1/2).
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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 21 Jun 2010, 09:25
Thank you for the explanation :)
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Re: Math: Triangles [#permalink] New post 06 Jul 2010, 05:00
Under Insoceles triangle section:
To find the base given the leg and altitude, use the formula:...

How do you derive these formulae? What's the logic behind them???
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Re: Math: Triangles [#permalink] New post 07 Jul 2010, 19:49
simply waoww.. wish i could have given you more than one +1...kudos :clap:
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Re: Math: Triangles   [#permalink] 07 Jul 2010, 19:49
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