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Constructing Triangles

Age 11 to 14
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Getting Started
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Constructing Triangles printable sheet


Take a ten-sided die (or other random number generating tools - a pack of cards with the picture cards removed, a calculator, a phone app...) and generate three numbers. Construct a triangle using these three numbers as the side lengths.

If you're not sure how to use a ruler and compasses to construct a triangle given the lengths of its three sides, watch the video below:
 


Generate a few more sets of numbers and draw some more triangles.
What do you notice?

Here are some questions you might like to consider:

  • Can you draw more than one triangle from each set of three numbers?
  • When is it possible to construct a triangle from the three numbers generated?
  • Is there a quick way to tell if it will be possible to construct a triangle?


Here is a game you could play:
Start with 10 points. Roll three dice. If a triangle can be drawn, you gain a point, if it can't, you lose a point. If you reach 20 points you win the game, if you reach 0 you lose.
Which is the more likely result?


Here is a game you could play with another person:
Player A chooses an integer length between 1 and 10cm. Player B randomly generates the lengths of the other two sides. If  a triangle can be drawn, Player B wins; otherwise they lose.
Is there a "best" length that Player A should choose?
Is this a fair game?


Now explore what happens if you generate 4 numbers and draw a quadrilateral.
 

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Trice

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

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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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