Dissect a Square into a set of Acute Triangles

Given a square. Dissect the area into a set of non-overlapping acute triangles.




Here is a GSP file if needed.







Hint and Exploration


What is the minumum number of acute triangles?

Things we may have learned

-- A single point in the center connected to the four vertices will not work-- right triangles are constructed.

-- Each vertex of the square must be divide by at least one line segment.

-- If segments radiate from an internal point that is not along a segment, then there must be at least 5 radii.

-- If a point is internal to a segment, there must be at least two segments radiating from the point on the same side.

-- Five acute triangles can fit together into a pentagon (not necessarily regular).



Additional Challenges:

1. Find a dissection with 8 acute triangles.

2. Find a dissection with 9 acute triangles.

3. Find two different dissections 10 acute triangles.

4. Find a dissection with 10 acute triangles where each of the acute triangles is isosceles.

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