Triangles

  • Shapely pairs
    problem
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    Shapely Pairs

    Age
    11 to 14
    Challenge level

    A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

  • Property chart
    problem
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    Property Chart

    Age
    11 to 14
    Challenge level

    A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

  • Isosceles Seven
    problem
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    Isosceles Seven

    Age
    14 to 16
    Challenge level

    Is it possible to find the angles in this rather special isosceles triangle?

  • Small pepper seedlings in turquoise pots.
    problem
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    Triangle Midpoints

    Age
    14 to 16
    Challenge level

    You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

  • Of all the areas
    problem
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    Of All the Areas

    Age
    14 to 16
    Challenge level

    Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

  • Triangle in a Triangle
    problem
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    Triangle in a Triangle

    Age
    14 to 16
    Challenge level

    Can you work out the fraction of the original triangle that is covered by the inner triangle?

  • Hexy-Metry
    problem
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    Hexy-Metry

    Age
    14 to 16
    Challenge level

    A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

  • Area I'n It
    problem

    Area I'n It

    Age
    16 to 18
    Challenge level
    Triangle ABC has altitudes h1, h2 and h3. The radius of the inscribed circle is r, while the radii of the escribed circles are r1, r2 and r3 respectively. Prove: 1/r = 1/h1 + 1/h2 + 1/h3 = 1/r1 + 1/r2 + 1/r3 .
  • Farhan's Poor Square
    problem

    Farhan's Poor Square

    Age
    14 to 16
    Challenge level
    From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.
  • Counting Triangles
    problem

    Counting Triangles

    Age
    11 to 14
    Challenge level
    Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
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