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?
A triangle has no diagonals.
A quadrilateral has two diagonals.
A pentagon has five diagonals.
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.
