Postulates and Theorems

[dheaven1]

I'm going over math basics and came across this lesson about Postulates and Theorems. To those familiar with the test or who have taken it previously, is this something I should spend time memorizing? Or would it be a waste of time? Basically, how much of the following do I really need to know for the GMAT?

Postulates and Theorems

1. If unequal quantities are added to unequal quantities of the same order, the result is unequal quantities in the same order.
2. If equal quantities are added to, or subtracted from, unequal quantities, the results are unequal in the same order.
3. If unequal quantities are subtracted from equal quantities, the results are unequal in the opposite order.
4. Doubles or halves of unequals are unequal in the same order.
5. If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
6. The sum of two sides of a triangle must be greater than the third side.
7. If two sides of a triangle are unequal, the angles opposite these sides are unequal, with the greater angle opposite the greater side.
8. If two angles of a triangle are unequal, the sides opposite these angles are unequal, with the greater side opposite the greater angle.
9. An exterior angle of a triangle is greater than either remote interior angle.

Thanks for your help as always.

Dave

[kstv]

Hi Dave
My humble opinion is GMAT format does not encourage memorising other than basics. Could like to know from others if they agree and if so what are the basics.

I could try to prove the theorems that you mention by pluggin values or reasoning them out but that cos' I hate mugging.
But, you cannot invent the wheel everytime like trying to prove pythagoras theorem in 2 min.

6. The sum of two sides of a triangle must be greater than the third side.
Try drawing a triangle where the third side is > the sum of other two sides.
It is obviously not possible.

9. An exterior angle of a triangle is greater than either remote interior angle.
Infact it is more imp to remember than the exterior angle is equal to sum of the two opposite interior angle.
Visually it is more obvious than proving it, still.
If the angles of a traingle are a,b,c let the exterior angle d be to c or supplement to c.
d= a+b then d will be = , < or >90° correspondinly c be be =,> and < 90°
if d=90° a+b = 90° so even if a is 1° b has to be 89° or less than d
if d<90° a+b =d so individually they will be less than d
if d> 90° c<d as c+d = 180°