Question

For every 10 yards on a football field, there is a boldly marked line labeled with the amount of yards. Each of those lines is perpendicular to both sidelines. What can be said about the relationship of the sidelines? Justify your answer.

a. The sidelines are perpendicular to each other by the definition of the Transitive Property.

b. The sidelines are parallel by the Same-Side Interior Angles Theorem.

c. The sidelines are perpendicular by the Perpendicular Transversal Theorem

d. The sidelines are parallel because they are perpendicular to the same line.

Answer 1

they are parallel, but why are they parallel

Answer 2

That's what I don't get!

Answer 3

can you tell me what the Same-Side Interior Angles Theorem is ?

Answer 4

any ideas?

Answer 5

then same-side interior angles are supplementary, yeah sorry my computer is being dumb.

Answer 6

good

Answer 7

so if you had two parallel lines, then the same-side interior angles are supplementary

Answer 8

that's fine if you know the two lines are parallel

BUT

if you had no idea they were parallel, then you can use this theorem

Answer 9

sure you can use the converse of this theorem, but that's not what choice B is saying

Answer 10

so what does that mean

Answer 11

It means that... If you don't know that these lines are parallel then you can't use this? Which means that if I do know they are, then the angles on the same side, they are interior supplementary?

Answer 12

yes you basically have it

if you know they are parallel, then the interior same side angles are supplementary and add to 180 degrees

but we don't know they are parallel (yet), so we can't use the Same-Side Interior Angles Theorem

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Sure we can use the converse, but we don't have that option in choice B. It's just the original theorem in choice B. So that's why choice B is incorrect and we can rule it out

Answer 13

So does that mean that choice C would be correct?

Answer 14

C) The sidelines are perpendicular...

is that true?

Answer 15

the side lines are perpendicular?

Answer 16

Right... I got my words mixed up...

Answer 17

that's ok, so choice C is out because the side lines are actually parallel

Answer 18

I think that choice D is correct though. Because it says they are parallel because they are perpendicual to the same line?

Answer 19

yes choice D is the correct answer for that exact reason

if any two lines are perpendicular to the same third line, then they must be parallel

Answer 20

Okay I get it now!

Answer 21

ok great