<p>this question was on the act free booklet practice exam. I reads
What is the maximum number of distinct diagonals that can be drawn in the hexagon shown below?
(then it has a picture fo a regular hexagon)</p>
<p>my answer was 6...the right answer is 9. I don't know why I am wrong</p>
<p>alright to do the questions with distinct DIAGONALS, do this:
(6 nCr 2)-6. use the number of sides, plug it into your calculator as 6 nCr (go to the MATH button and PRB and its number 3) 2. Then subtract the number of sides the figure has from the answer. This is because it says DISTINCT. </p>
<p>Alternately, draw lines from each of the corners of the shape connecting it to the corners forming visible lines, not lines that lie on the edges. If you ever get to a corner and go to draw a line to another corner and there is already a line there. Then don't retrace it.</p>
<p>Number of distinct diagonals in an n-gon is:</p>
<p>n * (n-3) / 2</p>
<p>So: 6 * (6-3) / 2 = 6 * 3 / 2 = 9</p>
<p>The OP's miscount may have been due to misunderstanding the definition of "diagonal". </p>
<p>In everyday usage, diagonal is often understood to mean "slanted" (as in the game of chess). However, in math, a diagonal is any line segment connecting non-adjacent vertices. He/she probably forgot to count the 3 "vertical and horizontal" diagonals.</p>
<p>You'll know you found all nine diagonals of a regular hexagon if you have a "Star of David" figure with 3 additional line segments connecting the opposite vertices.</p>