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help in geometry

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i do not understand the:

POSTULATE 9
P9: Through a point not on the line, one and only one line can be drawn parallel to the line.

Notice that point C is not on the line. Postulate 9 states that only one line can be drawn through point C and be parallel to the line.

this is off-topic

edit

also

THEOREM 3-14
In a plane, if two lines are perpendicular to a third line, then they are parallel to each other.

Given:
lt, mt

To Prove:
l | | m

Plan:
Use P10

off-topic
Aug 30, 2019
edited by travisio  Aug 30, 2019
edited by travisio  Aug 30, 2019

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Hi Travis! Hope you are alright.

Back on topic, I am going to answer the first one(terribly... I still tried... XD)

(the postulate numbers don't matter it's different for every textbook. I'm using Jergenson.)

OK, let's review what a parallel line means.

According to Study.com,

"The parallel postulate states that if a straight line intersects two straight lines forming two interior angles on the same side that add up to less than 180 degrees, then the two lines, if extended indefinitely, will meet on that side on which the angles add up to less than 180 degrees."

Ok, so that's the definition. Your thing says:

"P9: Through a point not on the line, one and only one line can be drawn parallel to the line.

Notice that point C is not on the line. Postulate 9 states that only one line can be drawn through point C and be parallel to the line.

Ok. Without a specified point, there are an infinite amount of lines possible.

Then you have one point that is given, but you can also make infinite lines from that point...

So, when we combine the facts, parallel and point C, we get a parallel line just hovering above the unnamed line.

Feel free to ask questions because I don't know where you are stuck and I just generalized it.

Sorry, I posted it so late...  + sorry for the bad answer...

Aug 31, 2019
edited by tommarvoloriddle  Aug 31, 2019
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+790
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thank you TMR this was helpfull(some) and the late timeing is not worriesome because i was just trying to get a better 'grip' on the postulate and therom

travisio  Aug 31, 2019