The three kinds of triangles are:
right triangle :one of the angles is a right angle (i.e. measures 90 degrees)
acute: All of the angles measures less than 90 degrees. A special case of acute is
the equiangular or equilateral triangle in which all angles measure 60 degrees;
obtuse: One of the angles measure more than 90 degrees.
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If you are talking about the common triangle puzzle, then there are 27 triangles. There are 16 one-cell triangles, 7 four-cell triangles, 3 nine-cell triangles, and 1 sixteen-cell triangle. There is a link to the pic for you also. _______________________________________________________________________ The answer in a two dimensional way would be 27. However, if you take into account that each triangle can be turned three ways, then you can understand that there are actually 81 triangles in all. THen you could ask the question, how many triangles can fit in this space (i.e. the picture)? The answer is the first level of infinitely many, or Aleph zero. This would be by finding the midpoint of each side of the all the 1- cell triangles and creating a new triangle.
If you have a grid of 5x5 squares you will have no triangles at all since there are no diagonal lines. * * * * * Here is a more likely answer - though I am not sure it is totally correct. A triangle is defined by three vertices. The total number of ways of picking 3 out of 25 points is 25*24*23/(3*2*1) 25 ways of picking a point from the grid at random, 24 ways to pick another point from the grid and 23 to pick the third. Divide by 3*2*1 since the order in which these collinear points is picked does not matter. However, some of these are not triangles: they are not triangles if all three points are in the same row or in the same column. Number of ways for that = 2*(25*4*3)/(3*2*1) 25 ways of picking a point from the grid at random, 4 ways of another point in the same row, 3 ways of picking the third in the same row. Divide by 3*2*1 since the order in which these collinear points is picked does not matter. Multiply by two because the same argument applies for collinearity in columns. So answer = 2300 - 100 = 2200
Several ways:Smallest 3 digit integerLog10(Googol)A perfect square
233468e4weduigfbeuJ
The three primary ways are: - writing an equation - drawing a diagram - reading a table