Pregunta
Which statement is true?
Seven diagonals can be drawn from each vertex of a nonagon.
Two diagonals can be drawn from each vertex of a quadrilateral.
Two diagonals can be drawn from each vertex of a pentagon.
Seven diagonals can be drawn from each vertex of a nonagon.
Two diagonals can be drawn from each vertex of a quadrilateral.
Two diagonals can be drawn from each vertex of a pentagon.
Ask by Bradley Hampton. in the United States
Jan 24,2025
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The third statement is true: Two diagonals can be drawn from each vertex of a pentagon.
Solución
Let’s analyze each statement based on the properties of polygons and their diagonals.
-
Seven diagonals from each vertex of a nonagon:
- A nonagon is a 9-sided polygon.
- The number of diagonals from each vertex of an n-gon is given by n - 3 (since you cannot draw a diagonal to itself or its two adjacent vertices).
- For a nonagon: 9 - 3 = 6 diagonals per vertex.
- This statement is false.
-
Two diagonals from each vertex of a quadrilateral:
- A quadrilateral is a 4-sided polygon.
- Using the formula: 4 - 3 = 1 diagonal per vertex.
- This statement is false.
-
Two diagonals from each vertex of a pentagon:
- A pentagon is a 5-sided polygon.
- Using the formula: 5 - 3 = 2 diagonals per vertex.
- This statement is true.
Answer: Only the third statement about the pentagon is true.
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Simplifique esta solución Extra Insights
Did you know that in a nonagon, which has nine sides, you can actually draw a total of 20 diagonals from each vertex? It seems a bit complex, but here’s a fun tip: The formula for finding the number of diagonals in a polygon is
When it comes to quadrilaterals, the statement is indeed false. In reality, from each vertex of a quadrilateral, you can draw one diagonal. Therefore, for a quadrilateral, there are exactly 2 diagonals in total. But don’t fret! A pentagon allows for more exciting connections with 5 diagonals in total, making geometry a lot more fun!
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