Parallel Lines 09

Table of Contents

  • Converse of Alternate Angles Test
  • Summary
  • What’s Next?

In the previous segment, we learnt about the Alternate angles test and proved it as well. In this segment, we will prove the converse of this test.

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    What is the Converse of the alternate angles test?

    The converse of alternate angles test states that if 2 lines are parallel, then the alternate angles formed by a transversal are congruent.

    Given: lines AB and CD are parallel to each other.

    Fig 1

    To Prove:

    ∠AGH ≅ ∠GHD

    We use indirect proof to prove this. That is, assume that alternate angles ∠AGH and ∠GHD are not congruent.

    For this, draw a line JK such that the alternate interior angles ∠JGH and ∠GHD are equal as shown below.

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