Geometry and Discrete math...if and then..?

Question

I'm having some trouble with my math...ok I have to determin which if and then statement is correct..
1) If two angles have equal measures then their complements have equal measure.
2) If the umbrella is torn then Jan will get wet.
3) If two angles of a triangle are equal then the sides opposite these angles are equal.
4) If d is less than 0 then d does not belong to the set of natural numbers.

Ok, I know that #2 is not true b/c it may not be raining
and I know #4 is true because natural numbers only contain positves
BUT..I don't know what #1 and #3 mean so please please help explain them to me. thanks a lot

Jerry...which can be detemined to be true or false

Answer 1

Do you mean which is a valid argument or which can be detemined to be true or false?

Edit:

1. False statement. The definition of complementary angles is two angles whose measures have the sum 90. Therefore, if one angle has a measure of 108 and is equal to a second angle, then a complement does not exist.

2. Not a statement. The sentence cannot be determined definitely true or definitely false.

3. True statement. However, this is not stated properly.
a. If two angles of a triangle are congruent, then the sides opposite those angles are congruent (or equal).
b. If the measures of two angles of a triangle are equal, then the sides opposite those angles are equal.

4. True statement. Natural numbers are defined as follows: N = {1, 2, 3, ...}.
Therefore, since d < 0, d is not a member of N.

Answer 2

1 and 3 are true, for #1 its saying if two angles are say 2 degrees there complimentary, which is the rest of the angle that would create a straight line would be 178 degrees for both 2+178=180, and #3 is saying in a triangle with angles ABC and sides abc (lower cased on purpose) each opposite the angles so angle A would be across from side a, its saying if A=B then a=b which is true, when two angles are the same it is called an isosceles triangle which has two same sides and two same angles. Hope that helps and I'm right.

Answer 3

Jerry has it right.The first problem says 2 angles not 2 angles of a triangle. Anyway, the measures of a triangle equal 180. The only way the angles can be complementary is if the triangle is a right triangle.

Answer 4

number 1 is true... because in geometry.. when 2 angles are equal then their complements have equal measures... ex... 30 degrees and 30 degrees.... the complement of 30degrees is 90-30+60 degrees... the other 30.... 90-30=60 deg...

both of their complements are 60... so it is equaL..

number 3 is also true because if 2 angles of a triange is congruent then it is an isosceles triangle... and there is a theorem in isosceles triangle known as the (CITT) or Converse of Isosceles triangle theorem.. it states that if 2 angles of a triangle are equal, then, then the sides opposite the angles are congruent

Answer 5

1) true - if each angle is x, then both of their complements are 90-x
2) unable to be determined since Jan may not even be outside
3) true, this forms an isoceles triange which means opposite sides will have equal length
4) true, natural numbers are 1, 2, 3, etc... (no negatives)

Answer 6

its friday night. why are you doing homework lol