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A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

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Quad in Quad

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

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The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?

Same Length

Age 11 to 16 Challenge Level:
For each problem, draw yourself a nice clear diagram.

Here are some useful questions to ask yourself when working on geometry proofs:
  • What angles do you know? (Mark them on your diagram.)
  • Which lengths are equal? (Mark them on your diagram.)
  • Which unknown angles are equal? How do you know?
  • Are there any congruent triangles?