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Which of the following statements about the diagonals of a polygon is correct?

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Question: Which of the following statements about the diagonals of a polygon is correct?

Options:

  1. A triangle has no diagonals.
  2. A quadrilateral has two diagonals.
  3. A pentagon has five diagonals.
  4. A hexagon has nine diagonals.

Correct Answer: A triangle has no diagonals.

Solution: 

A triangle has no diagonals, as it has only three vertices. The formula for the number of diagonals in a polygon is n(n-3)/2, where n is the number of sides.

Which of the following statements about the diagonals of a polygon is correct?

Practice Questions

Q1
Which of the following statements about the diagonals of a polygon is correct?
  1. A triangle has no diagonals.
  2. A quadrilateral has two diagonals.
  3. A pentagon has five diagonals.
  4. A hexagon has nine diagonals.

Questions & Step-by-Step Solutions

Which of the following statements about the diagonals of a polygon is correct?
  • Step 1: Understand what a diagonal is. A diagonal is a line segment that connects two non-adjacent vertices in a polygon.
  • Step 2: Identify the number of vertices in a triangle. A triangle has 3 vertices.
  • Step 3: Determine if a triangle has any diagonals. Since a triangle has only 3 vertices, there are no non-adjacent vertices to connect, so it has no diagonals.
  • Step 4: Learn the formula for finding the number of diagonals in any polygon. The formula is n(n-3)/2, where n is the number of sides (or vertices) of the polygon.
  • Step 5: Apply the formula to a triangle. For a triangle, n = 3. Plugging this into the formula gives: 3(3-3)/2 = 3(0)/2 = 0. This confirms that a triangle has no diagonals.
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