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1965 AMC 12 Question 25

AMC12 · 1965 AMC 12

Question 25

Let $ABCD$ be a quadrilateral with $AB$ extended to $E$ so that $AB=BE.$ Lines $AC$ and $CE$ are drawn to form angle $ACE.$ For this angle to be a right angle it is necessary that quadrilateral $ABCD$ have:
  1. all angles equal
  2. all sides equal
  3. two pairs of equal sides
  4. one pair of equal sides
  5. one pair of equal angles