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anonymous

  • one year ago

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∠SQV + m∠VQT = 180° Substitution Property of Equality II m∠SQT = 180° Definition of a Straight Angle III m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate m∠VQT + m∠ZRS = 180

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  1. mathstudent55
    • one year ago
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  2. anonymous
    • one year ago
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  3. mathstudent55
    • one year ago
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    In Geometry, you make some assumptions and you call them postulates or axioms. You make a minimum number of postulates. Then using postulates and definitions, you prove theorems. The way I learned Geometry, corresponding angles of parallel lines are congruent is a postulate. From there I was given the theorems of alternate interior and exterior angles, and same sides interior angles. In your case, if you are proving that corresponding angles are congruent, that must be a theorem for you . That means something else that was a theorem for me must have been a postulate for you.

  4. mathstudent55
    • one year ago
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    In the lines labeled I, II, and III, are you supplying both statements and reasons?

  5. anonymous
    • one year ago
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    It says written in the correct order

  6. mathstudent55
    • one year ago
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    How exactly was this problem given to you and how much have you filled in yourself?

  7. mathstudent55
    • one year ago
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    In other words, can you show exactly how the problem was given before you started working on it?

  8. anonymous
    • one year ago
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    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∠SQV + m∠VQT = 180° Substitution Property of Equality II m∠SQT = 180° Definition of a Straight Angle 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

  9. mathstudent55
    • one year ago
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    Ok. What you have to do is decide the correct order of the lines labeled I, II, and III? All the other lines are where they belong?

  10. mathstudent55
    • one year ago
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    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∠SQV + m∠VQT = 180° Substitution Property of Equality II m∠SQT = 180° Definition of a Straight Angle 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

  11. mathstudent55
    • one year ago
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    Ok. Line III goes first. Then line II. Then line I.

  12. anonymous
    • one year ago
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    thank you :)

  13. mathstudent55
    • one year ago
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    Statements Reasons segment UV is parallel to segment WZ Given Points S, Q, R, and T all lie on the same line Given III m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate II m∠SQT = 180° Definition of a Straight Angle I m∠SQV + m∠VQT = 180° Substitution Property of Equality 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

  14. mathstudent55
    • one year ago
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    You're welcome.

  15. anonymous
    • one year ago
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    that isnt an answer

  16. mathstudent55
    • one year ago
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    You can also have II first, then III, then I.

  17. anonymous
    • one year ago
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    thanks

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