GREATER CHALLENGES II 

3rd year of secondary education 


1.
SQUARE GRIDS AND
ANGLES IN A TRIANGLE


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.



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. 

2. THE CHALLENGE


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.



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).





















Josep Mª Navarro Canut 


ProyectoDescartes.org. Year 2013




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