NAME DATE PERIOD 35 Skills Practice Proving Lines Parallel Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer.

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  1. Click ‘Get Form’ button to access the Proving Lines Parallel Practice. This action will allow you to view and edit the document in an online format.
  2. Begin by filling in your name in the designated NAME field at the top of the form. This will help identify your submission once completed.
  3. Next, enter the current DATE in the appropriate section to indicate when you are completing the practice.
  4. In the PERIOD field, specify your class period. This information can help your instructor track submissions more efficiently.
  5. Read the instructions carefully for each problem regarding the relationships between angles. For example, state which lines are parallel, referencing the appropriate postulate or theorem.
  6. Work through the provided angle relationships, such as ∠3 ≅ ∠7 and ∠9 ≅ ∠11, and justify your answers based on the properties of parallel lines.
  7. Solve for any unknown variables, such as x. Make sure to show all your work in the spaces provided to demonstrate your reasoning.
  8. Review all your entries to ensure accuracy and completeness before finalizing the document.
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What is the 3 parallel lines theorem?

Three Parallel Lines Theorem If three parallel lines intersect two transversals, then they divide the transversals proportionally.

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel. Converse of the Alternate Interior Angles Theorem: If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

Ways to Prove Lines Are Parallel the converse of the alternate interior angles theorem. the converse of the corresponding angles theorem. the converse of the same-side interior angles postulate. the converse of the alternate exterior angles theorem.

Properties of Parallel Lines Corresponding angles are equal. Vertical angles/ Vertically opposite angles are equal. Alternate interior angles are equal. Alternate exterior angles are equal. Pair of interior angles on the same side of the transversal are supplementary.

If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel. If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel.

The definition of parallel lines, in Euclid's wording, is that of “straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction”.

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