anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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mathstudent55
  • mathstudent55
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anonymous
  • anonymous
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mathstudent55
  • mathstudent55
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.

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mathstudent55
  • mathstudent55
In the lines labeled I, II, and III, are you supplying both statements and reasons?
anonymous
  • anonymous
It says written in the correct order
mathstudent55
  • mathstudent55
How exactly was this problem given to you and how much have you filled in yourself?
mathstudent55
  • mathstudent55
In other words, can you show exactly how the problem was given before you started working on it?
anonymous
  • anonymous
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
mathstudent55
  • mathstudent55
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?
mathstudent55
  • mathstudent55
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
mathstudent55
  • mathstudent55
Ok. Line III goes first. Then line II. Then line I.
anonymous
  • anonymous
thank you :)
mathstudent55
  • mathstudent55
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
mathstudent55
  • mathstudent55
You're welcome.
anonymous
  • anonymous
that isnt an answer
mathstudent55
  • mathstudent55
You can also have II first, then III, then I.
anonymous
  • anonymous
thanks

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