Similarity and congruence

  • Matching Triangles
    problem
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    Matching triangles

    Age
    5 to 7
    Challenge level
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    Can you sort these triangles into three different families and explain how you did it?

  • Is a Square a Rectangle?
    problem

    Is a square a rectangle?

    Age
    7 to 11
    Challenge level
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    How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
  • Number the Sides
    problem

    Number the sides

    Age
    7 to 11
    Challenge level
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    The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
  • Pinhole Camera
    problem

    Pinhole camera

    Age
    11 to 14
    Challenge level
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    Make your own pinhole camera for safe observation of the sun, and find out how it works.
  • Same length
    problem
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    Same length

    Age
    11 to 16
    Challenge level
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    Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

  • Triangle in a Trapezium
    problem
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    Triangle in a trapezium

    Age
    11 to 16
    Challenge level
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    Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

  • Pythagoras Proofs
    problem
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    Pythagoras proofs

    Age
    11 to 16
    Challenge level
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    Can you make sense of these three proofs of Pythagoras' Theorem?

  • Making sixty
    problem
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    Making sixty

    Age
    14 to 16
    Challenge level
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    Why does this fold create an angle of sixty degrees?

  • Geometry and Measure - Short Problems
    problem

    Doubly isosceles

    Age
    14 to 16
    Challenge level
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    Find the missing distance in this diagram with two isosceles triangles

  • Triangle midpoints
    problem
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    Triangle midpoints

    Age
    14 to 16
    Challenge level
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    You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?