Use the figure to answer the question that follows: segments uv and wz are parallel with line st intersecting both at points q and r respectively when written in the correct order, the two-column proof below describes the statements and reasons for proving that corresponding angles are congruent: statements reasons segment uv is parallel to segment wz given points s, q, r, and t all lie on the same line. given m∠sqt = 180° definition of a straight angle m∠sqv + m∠vqt = m∠sqt angle addition postulate m∠sqv + m∠vqt = 180° substitution property of equality i m∠sqv + m∠vqt − m∠vqt = m∠vqt + m∠zrs − m∠vqt m∠sqv = m∠zrs subtraction property of equality ii m∠sqv + m∠vqt = m∠vqt + m∠zrs substitution property of equality iii m∠vqt + m∠zrs = 180° same-side interior angles theorem ∠sqv ≅ ∠zrs definition of congruency

The order of the start of the proof seems fine; we're to choose the next steps I guess.

segment UV is parallel to segment WZ Given

Points S, Q, R, and T all lie on the same line. Given

m∠SQT = 180° Definition of a Straight Angle

m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate

m∠SQV + m∠VQT = 180° Substitution Property of Equality

That's all valid up to here. It seems to me sort of the hard way to get to linear supplements but here we are.

ZRS is mentioned in the rest of the lines; let's find the one that comes first.

III m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem

Now we have two things equal to 180 degrees, so they're equal to each other.

II m∠SQV + m∠VQT = m∠VQT + m∠ZRS Substitution Property of Equality

Now comes

I m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT

m∠SQV = m∠ZRS Subtraction Property of Equality

And we conclude,

∠SQV ≅ ∠ZRS Definition of Congruency

The corresponding angles formed by two parallel lines, having the same  transversal are congruent

The correct order of the statements are;

The reason the above statements are in the correct order is as follows:

The two column proof is presented as follows;

Statements                                                          Reason

Segments UV is parallel to segment WZ           Given

Points S, Q, R, and T all lie on the same line      Given

m∠SQT = 180°                                                       Definition of a straight angle

m∠SQV + m∠VQT = m∠SQT                                 Angle Addition Postulate

m∠SQV + m∠VQT = 180°                            Substitution Property of Equality

III m∠VQT + m∠ZRS = 180°                          Same-side interior angle theorem

II m∠SQV + m∠VQT = m∠VQT + m∠ZRS    Substitution Property of Equality

I m∠SQV + m∠VQT - m∠VQT = m∠VQT

+ m∠ZRS - m∠VQT                                       Subtraction Property of Equality

m∠SQV = m∠ZRS                                      

m∠SQV ≅ m∠ZRS                                       Definition of Congruency

Therefore, the correct order is as follows;

First

Second

Third

Learn more about the angles formed by two parallel lines here:

link

so far i think you have the right thing going for you just remember soh cah toh

step-by-step explanation:

sine over hypotenuse

cosine   equals adjacent

tangent over hypotenuse