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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,

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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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I withdrawn these rules as well as some other properties and formulas (there are plenty of them), as GMAT problems doesn't require knowing them for solving.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.
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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 ?

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.

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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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?

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

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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