Question

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

Answer 1

http://assets.openstudy.com/updates/attachments/4fb80c47e4b05565342d71e1-steelersbabe31-1337461883428-hh.jpg

Answer 2

Write a paragraph to prove that the measure of angle 3 is equal to the measure of angle 5.

Answer 3

This is what i have so far : It is given that transversal t intersects parallel lines PQ and RS.

Answer 4

are you allowed to use "alternating interior angles"?

Answer 5

yes

Answer 6

After you prove the two lines are parallel, then you can just finish it with "alternate interior angles" and then you're done.

Answer 7

Why would you need a paragraph for that? Two sentences, really.

Answer 8

i know but it asks for a paragraph proof :(

Answer 9

It is given that transversal t intersects parallel lines PQ and RS.Angle 1 and angle 4 equals 180 by the definition of supplementary angles. Angle 5 and 8 is equal to 180 by the definition of supplementary angles. Angle 1 and 5 are the same measure using the corresponding angles postulate. Therefore, angle 3 is equal to the measure of angle 5 by alternate interior angles.

Answer 10

Is this correct @jbell0385

Answer 11

mmm. I guess that's up to your teacher, but to me it doesn't make sense to use corresponding angles to prove alternate interior angles. If you use corresponding angles, then you might as well just jump straight to alternate interior angles.

Answer 12

It is given that transversal t intersects parallel lines PQ and RS.Angle 1 and angle 4 equals 180 by the definition of supplementary angles. Angle 5 and 8 is equal to 180 by the definition of supplementary angles.. Therefore, angle 3 is equal to the measure of angle 5 by alternate interior angles.

Answer 13

hah sure. but would your teacher not accept it if you just wrote:

It is given that transversal t intersects parallel lines PQ and RS. Therefore, angle 3 is congruent to angle 5 by the alternate interior angles theorem.

Answer 14

probably i know that's right .

Answer 15

Thank you !:) @jbell0385

Answer 16

no problem, good luck on your proofs.