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GREATER CHALLENGES -II |
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3rd year of secondary education |
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1. SQUARE GRIDS AND
ANGLES IN A TRIANGLE |
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In
this window, as in the first window on the previous page, there is a square
grid
and a triangle drawn on it. However, this time instead of focusing on the
shape's area
we are going to study its angles.
The electronic board works in a similar way to before. The question that you
should aim to answer by the end of the unit is found in the last activity. |
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1.- Draw
different triangles on the electronic board making sure that angle BAC
is one of its acute angles in each case. For each triangle write down
the size of angle A the lengths of the height and line AD
and the ratio between these two lengths in your exercise book. Draw a
table in your book to help you. |
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2. THE CHALLENGE |
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In
this window you can move the vertices
of the triangle to any of the points on the grid,
using the mouse. You will need to carry out a fairly complex mathematical
investigation at home in order to be able to answer the last two questions. So
be patient and good luck! Big
clue: If angle BAC is 60º, the relationship between the perpendicular
height from point C (or from point B) and the distance from point A to the
base of the perpendicular height is equal to the square root of 3. |
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2.- Repeat
the above activity for different triangles that you draw on the electronic
board changing vertices B and/or C, making sure that angle A
is always acute (this angle is used as our point of reference). 3.- Use
the information from the activities above to help you answer the following
question: Is it possible to draw a triangle where angle BAC is 60º? 4.- Is
it possible to draw equilateral triangles on a square grid where each of the
triangle's vertices is located on a point on the grid? (Another way of
asking this question is to ask if it is possible to make an equilateral
triangle with a rubber band on a board with pins arranged like the points
on a square grid, regardless of the number of pins per side). |
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Josep Mª Navarro Canut |
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Spanish Ministry of Education. Year 2001 |
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