if A=B then B=C then A=C in geomety?

Question

ok so i have a quetion about geometry this is a proof
given A II B, B II C
prove A II C

parrle line's- A,B,C
A
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B
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C
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im trying to prove that transitive property to my teacher that im right and the math book is wrong
Transitive property is if two quantities are equal to the same quantity, then they are equal to each other: if A=B and B=C then A=c.

doesn't this property work with parrle lines ?
and i wright?

Answer 1

Yes it works with parallel lines

Answer 2

A transitive relation is one where if the first thing relates to the second and the second relates to the third, then the first relates to the third.

Some example of transitive relations are

"Equals":
If A = B and B = C, then A = C

"Less than":
If A < B and B < C, then A < C

"Multiple of"
If A is a multiple of B and B is a multiple of C, then A is a multiple of C.

"Subset of"
If A is a subset of B and B is a subset of C, then A is a subset of C.

So your question about whether "parallel to" is a transitive relation means you have to decide whether the following statement is true about a line A, a line B, and a line C:
If A is parallel to B and B is parallel to C, then A is parallel to C.

This would be true if A, B, and C were three different lines. But for transitivity, the statements has to be true regardless of whether they are all different or not. This is where it is a tricky question.

If A and B are two parallel lines, and C = A, then we can correctly say
A is parallel to B and B is parallel to C.
But it would be false to say that
A is parallel to C.
(The reason being that A is equal to C, not parallel to C.)

So the "parallel" relation is "almost transitive" but not quite, because of this one tricky circumstance. In mathematics, we have to always be absolutely precise in our language. There is no room for ambiguity or exceptions to our statements. "Almost" doesn't count.

Answer 3

if you draw a line through line A, B, C
then you can show that their corresponding angles are concurrent between A and B, and then B and C,
so A and C by substitutions. then A//C

Answer 4

I dont know ... sound like u r right .... but A and C mayb the same line

Answer 5

99.9% correct

Answer 6

yes. this is true.

Answer 7

_____ _____ _____ _____ _____ _____
| | | | | | | | | | | |
| A | = | B | | A | = | C | | B | = | C |
|____ | |____| |____| |____| |____| |____|