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For younger learners

  • Early Years Foundation Stage

Angles, Polygons and Geometrical Proof Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Angles, Polygons and Geometrical Proof Age 11-14 and Age 14-16.

Printable worksheets containing selections of these problems are available here:

Stage 3 ★ Sheet 1 Solutions
  Sheet 2 Solutions
  Sheet 3 Solutions
  Sheet 4 Solutions
     
Stage 3 ★★ Sheet 1 Solutions
  Sheet 2 Solutions
  Sheet 3 Solutions
     
Stage 4 ★★ Sheet 1 Solutions
  Sheet 2 Solutions
     
Stage 4 ★★★ Sheet 1 Solutions

Overlapping Annuli

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

Just from the diagram, can you work out the radius of the smaller circles?

Altitude Inequalities

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

Weekly Problem 8 - 2010
Are you able to find triangles such that these five statements are true?

Semicircle in a Triangle

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

A semicircle is drawn inside a right-angled triangle. Find the distance marked on the diagram.

Circled Square

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

Can you find the area of this square inside a circle?

Folded Square

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

This square piece of paper has been folded and creased. Where does the crease meet the side AD?

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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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