Question

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
I m∠SQT = 180° Definition of a Straight Angle
II m∠SQV + m∠VQT = 180° Substitution Property of Equality
III m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate
m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem
m∠SQV + m∠VQT = m∠VQT + m∠ZRS Substitution Property of Equality
m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT
m∠SQV = m∠ZRS Subtraction Property of Equality
∠SQV ≅ ∠ZRS Definition of Congruency
Which is the most logical order of statements and reasons I, II, and III to complete the proof? (5 points)


I, III, II
II, I, III
II, III, I
III, I, II

《THE CORRECT ANSWER IS I, III, II GUYS》
i'm just posting bc i havent seen the correct ans for this ques on brainly yet !

Answer 1

Answer:

Using the formulas of Congruency, we find that the correct order of the statements are;

III m∠VQT + m∠ZRS = 180°

II m∠SQV + m∠VQT = m∠VQT + m∠ZRS

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

Step-by-step explanation:

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

The correct order of the statements are;

III m∠VQT + m∠ZRS = 180°

II m∠SQV + m∠VQT = m∠VQT + m∠ZRS

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

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

III m∠VQT + m∠ZRS = 180°; Given that m∠VQT and  m∠ZRS are same side interior angles

Second

II m∠SQV + m∠VQT = m∠VQT + m∠ZRS;    By Substitution Property of Equality given that both (m∠SQV + m∠VQT), (m∠VQT + m∠ZRS) are equal to 180°

Third

I m∠SQV + m∠VQT - m∠VQT = m∠VQT  m∠ZRS - m∠VQT; The same value - m∠VQT is subtracted from both sides of the equation in Step II, therefore, both sides of the equation remains equal

For more explanation, refer the following link:

https://brainly.com/question/10714836

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