Question
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.
Ask by Bradley Hampton. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The third statement is true: Two diagonals can be drawn from each vertex of a pentagon.
Solution
Let's analyze each statement based on the properties of polygons and their diagonals.
1. **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.**
2. **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.**
3. **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.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution 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 \(\frac{n(n-3)}{2}\), where ‘n’ is the number of sides. So for a nonagon, it's \(\frac{9(9-3)}{2} = 20\). 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!
