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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?

Quad in Quad

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

Arrowhead

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?
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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