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# Math: Triangles

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Manager
Joined: 22 Sep 2009
Posts: 212
Location: Tokyo, Japan

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24 Nov 2009, 22:58
Thank you so much.
This is massive
Intern
Joined: 28 May 2008
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08 Dec 2009, 15:33
Thank you for the awesome post..
Intern
Joined: 22 Dec 2009
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27 Dec 2009, 05:51
2
KUDOS
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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Joined: 02 Sep 2009
Posts: 43789

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27 Dec 2009, 06:04
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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Joined: 24 Jul 2009
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Schools: Mellon, USC, MIT, UCLA, NSCU

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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.
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Manager
Joined: 27 Aug 2009
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12 Jan 2010, 16:43
Thanks a lot really good summary
Manager
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Schools: Mellon, USC, MIT, UCLA, NSCU

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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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Manager
Joined: 25 Dec 2009
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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 ?
Manager
Joined: 25 Dec 2009
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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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14 Jan 2010, 16:16
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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14 Jan 2010, 16:47
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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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.

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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Manager
Joined: 14 Feb 2010
Posts: 58
Location: Tokyo

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15 Feb 2010, 00:01
excellent post! thanks a lot Bunuel!
Manager
Joined: 30 Jun 2004
Posts: 175
Location: Singapore

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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?
Manager
Joined: 21 Feb 2010
Posts: 205

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05 Jun 2010, 05:05
Intern
Joined: 14 May 2010
Posts: 5

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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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18 Jun 2010, 01:14
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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21 Jun 2010, 09:25
Thank you for the explanation
Manager
Joined: 23 Oct 2009
Posts: 84
Location: New Delhi, India
Schools: Chicago Booth, Harvard, LBS, INSEAD, Columbia

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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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07 Jul 2010, 19:49
simply waoww.. wish i could have given you more than one +1...kudos
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Re: Math: Triangles   [#permalink] 07 Jul 2010, 19:49

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