The figure below shows a transversal t which intersects the parallel lines PQ and RS.

Write a paragraph to prove that the measure of angle 4 is equal to the measure of angle 8.

Question

The figure below shows a transversal t which intersects the parallel lines PQ and RS. 

Write a paragraph to prove that the measure of angle 4 is equal to the measure of angle 8.

anonymous · Answer

attachment

uh60blackhawk · Answer

oh i hate prove

anonymous · Answer

Me too. I suck at them

uh60blackhawk · Answer

ill try help not sure i am going get it right

uh60blackhawk · Answer

well first of 4 and 6 is a transversal

uh60blackhawk · Answer

sorry trying to help two people

uh60blackhawk · Answer

So ange 4 and ange 6 is a transverse so that mean angle 4 and 2 are congruent

anonymous · Answer

That's fine. Take your time

uh60blackhawk · Answer

and angle 6 and 8 are congruent too.

uh60blackhawk · Answer

so this proves that 4 and 8 are congruent too.

uh60blackhawk · Answer

And i think that will be it but it

uh60blackhawk · Answer

@Compassionate am i correct on this prove?

uh60blackhawk · Answer

Oh i forgot to add the 4 and 6 is transverse that mean that line PQ and RS are parallel

uh60blackhawk · Answer

do you understand if not i can rewrite the prove.

anonymous · Answer

So the proof in paragraph form would be 

Angles 4 and angles 6 is a transversal. Since angle 4 and angle 6 are transverse, that means that line PQ and RS are parallel.  This means that angles 4 and 2 and angles 6 and 8 are congruent. This proves that angle 4 and angle 8 are congruent.??

uh60blackhawk · Answer

yes that will be correct but make sure that i am right. little rusty on my proves

anonymous · Answer

@charlotte123 @wolfe8

would that be right?

shamil98 · Answer

Nope.. 4 and 6 are on lines that are parallel...

anonymous · Answer

So should I take that part out completely?

shamil98 · Answer

This means that angles 4 and 2 and angles 6 and 8 are congruent.
eh this also incorrect.
those angles are congruent because of the vertical angle theorem.

uh60blackhawk · Answer

but i thought angle 4 and 6 can prove it is a transversal

uh60blackhawk · Answer

when you proof that 4 and 6 a traversal you can prove that line pq an rs are parallel

shamil98 · Answer

4 and 8 are congruent using the transitive property.
<4 = <6
<6 = <8
<4 = < 8

shamil98 · Answer

<4 = <6 ( alternate interior angles )
<6 = <8 ( vertical angle theorem )
<4 = <8 ( transitive property)

uh60blackhawk · Answer

yea i shamil98 is correct.

anonymous · Answer

Angle 4 is congruent to angle 6 because they are alternate interior angles. Angle 6 is congruent to angle 8 by the vertical angle theorem. Angle 4 is congruent to angle 8 by the transitive property.

anonymous · Answer

So would that be correct?

uh60blackhawk · Answer

yes

uh60blackhawk · Answer

this picture i am going attach going help you through parallelgram

anonymous · Answer

Thank you so much!