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Re: Math: Triangles [#permalink]
27 Dec 2009, 05:51
1
This post received 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,
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. _________________
Re: Math: Triangles [#permalink]
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,
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I withdrawn these rules as well as some other properties and formulas (there are plenty of them), as GMAT problems doesn't require knowing them for solving.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. _________________
Re: Math: Triangles [#permalink]
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 ?
Re: Math: Triangles [#permalink]
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.
Re: Math: Triangles [#permalink]
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. _________________
Re: Math: Triangles [#permalink]
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?
Re: Math: Triangles [#permalink]
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]
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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