Geometry Question?

Question

Determine whether the statement is always true, sometimes true, or never true & please explain why or why not.

a. Two lines that are parallel to a third line are parallel to each other.
b. A triangle contains at least two acute angles.
c. Vertical angles are complementary angles.

Answer 1

A. true because they would have to have the same slope for them to be parallel to the same line
B.true because if you had more than one right or obtuse angle then you can not form a triangle
C. I'm sorry but i don't know

Answer 2

a. Always true.
Assume the opposite, that the two lines are not parallel and thus intersect each other. Then the two lines cannot both be parallel to a third line, because if that third line is parallel to one line, it will intersect the other line.

b. Always true.
Assume the opposite, that it is possible for a triangle to have only one acute angle, thus the other two angles must be right or obtuse. If so, both must measure 90 degrees or greater, and their sum would equal or exceed 180. Since in every triangle, the sum of measures of the interior angles equals 180, the remaining angle would have to measure 0 degrees or less, which is impossible. So this case cannot exist.

c. Sometimes true.
If two vertical angles both measure 45 degrees, they are complementary (their measures add up to 90 degrees). Counterexample: if two vertical angles both measure 90 degrees, they add up to 180 degrees and are supplementary not complementary.

Answer 3

A. Some times true,

look at this, http://www.cs.unm.edu/~joel/NonEuclid/parallel.html

B. Always True,

It's important to note that a triangle has to always have at least two acute angles. Since the total of the three angles is always 180 degrees, it would be impossible to have two obtuse angles since those two alone would be more than 180. It would be impossible to have 2 right angles since they would total 180 and there would be nothing left for the third angle. Similarly, a right and an obtuse angle in the same triangle is impossible since they would total more than 180 degrees.

C,
Sometimes,
Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees

Answer 4

a. always because if they are parallel to a 3rd line, they must be parallel to eachother
b. always because a triangle cannot (impossible) have 2 right or obtuse angles
c. sometimes because vertical angles can also add up to more than 90 degrees or less than 90 degrees which would not make them complementary

Answer 5

a. always
reason - (postulate/theorem) If 2 lines are parallel to the same line, then they are parallel to each other.

b. always
reason - the angles add up to be 180. you can't have 2 angles that are both over 90 degrees because that would add up to over 180, without the third side.

c. sometimes
reason - vertical angles are congruent. they are only complementary when they are 45 degrees (adding up to 90). they are always congruent but are only complementary if they are 45 degrees.

Answer 6

in truth, the in common words situation that i visit discover in common with sacred geometry and alchemy is they both manage kinds of spirituality. Sacred geometry deals with using geometric kinds and shapes interior the layout and structure of church homes, temples, mosques or everywhere of non secular amassing. those particular shapes mean particular issues, reckoning on the religion or conception gadget. as an example, the pentagram in Christianity refers back to the 5 senses. In Catholicism, it may often times communicate over with the devil, or the Evil One. Alchemy deals with the technique of turning metals into gold, utilizing chemical substances and technology. even with the undeniable fact that, Alchemy is likewise a conception in searching the finest understanding by chemistry. subsequently, alchemy is a spirituality all its own. All in all, the in common words situation that i visit work out in common between both is they both manage a form, or varieties, of spirituality.

Answer 7

The answer has to be a.