Answers

  1. Always true.
  2. Sometimes true.
  3. Always true.
  4. Always true.
  5. Always true.
  6. Never true.
  7. Must be a rectangle (and therefore a parallelogram), could be a square.
  8. Must be a quadrilateral. Could be a kite, parallelogram, rectangle, rhombus, or square depending on which sides are congruent and additional properties.
  9. Possible conjectures: diagonals are perpendicular, one diagonal bisects the other, one diagonal bisects its angles.
  10. Possible conjectures: diagonals are congruent, diagonals bisect each other.
  11. Possible conjectures: diagonals are perpendicular, diagonals bisect each other.
  12. Possible conjecture: one pair of opposite angles are congruent.