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How to drive the formula of the number of triangles on a polygon that are derived from each of the diagonals if we have it?

a. Use the Pythagorean theorem.
b. Count the number of diagonals and apply a formula.
c. Use the law of sines and cosines.
d. Not enough information provided.

User AgRizzo
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1 Answer

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Final answer:

To determine the number of triangles formed by diagonals in a polygon, count the diagonals and apply the formula, n(n-3)/2, where 'n' is the number of sides of the polygon.

Step-by-step explanation:

The correct way to derive the formula for the number of triangles in a polygon that can be formed from its diagonals is by counting the number of diagonals and applying a formula. This approach involves understanding that a polygon with 'n' sides (an 'n-gon') will have 'n-3' triangles for each vertex after drawing all the diagonals from it. The total number of triangles from all the vertices is then given by 'n(n-3)/2' since each triangle is counted twice. The Pythagorean theorem is not relevant in this scenario since it is used to calculate the length of a side in a right triangle given the lengths of the other two sides.

User AfterFray
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