How many triangles are formed when you draw all the possible...

How many triangles are formed when you draw all the possible diagonals from just one vertex of a 35-gon? CAN'T COPY THE FIGURE $$\begin{array}{|l|c|c|c|c|c|c|c|c|}\hline \text { Number of sides } & 3 & 4 & 5 & 6 & \dots & n & \dots & 35 \\\hline \text { Number of triangles formed } & & & & & \dots & & \dots & \\ \hline\end{array}$$

How many triangles are formed when you draw all the possible diagonals from just one vertex of a 35-gon?
CAN'T COPY THE FIGURE
$$\begin{array}{|l|c|c|c|c|c|c|c|c|}\hline \text { Number of sides } & 3 & 4 & 5 & 6 & \dots & n & \dots & 35 \\\hline \text { Number of triangles formed } & & & & & \dots & & \dots & \\
\hline\end{array}$$

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Key Concepts

Triangulation

Triangulation is the process of dividing a polygon into triangles by drawing non-intersecting diagonals. When all possible diagonals are drawn from one vertex, the polygon is partitioned into exactly (n - 2) triangles, where n is the number of sides of the polygon. This method is fundamental in simplifying the analysis of polygons and has applications in calculating areas and in computer graphics.

Polygon

A polygon is a closed two-dimensional shape formed by a finite number of straight line segments connected end-to-end. The study of polygons includes analyzing their properties such as the number of sides, vertices, and the interior angles, which are foundational in understanding many geometric constructions and calculations.

Diagonal

A diagonal in a polygon is a line segment that connects two non-adjacent vertices. Drawing diagonals helps in dividing complex polygons into simpler components like triangles, and in many geometric problems, analyzing the properties and the number of resulting elements from these constructions is crucial.

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