Parallel line proofs

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  1. Relationships between lines and angles
  1. What is the value of x if AB‾\overline {AB} ∥\parallel CD‾\overline {CD} ?

    1. Parallel line proofs: using alternate alternate interior angles theorem to find unknown

    2. Parallel line proofs: solving for x by corresponding angles theorem

    3. Parallel line proofs: solve unknown by applying corresponding angles theorem
  2. Determine if enough information is given to prove p∥p \parallel qq State the postulates or theorems you use in your answers.

    1. Prove parallel lines by alternate exterior angles converse

    2. Parallel line proofs without enough information

    3. Proving parallel line using consecutive interior angles converse

    4. Parallel line proofs
  3. Prove that if two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel. (Prove the Alternate Exterior Angles converse)
    1. Write a two-column proof.
      1. Given: m∥m \parallel nn, ∠1\angle 1 ≅\cong∠2\angle 2
        Prove: s∥s \parallel tt
        Writing a two-column proof to prove parallel lines
      2. Given: ∠1\angle 1 ≅\cong∠2\angle 2, ∠1\angle 1 ≅\cong∠3\angle 3
        Prove: AB‾\overline {AB} ∥\parallel CD‾\overline {CD}
        Parallel line proofs in a two-column proof
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