How many diagonals does a triangle have?

(a) 0

(b) 1

(c) 2

(d) 3

To determine how many diagonals a triangle has, let's first clarify what a diagonal is. A diagonal is a line segment that connects two non-adjacent vertices of a polygon. In the case of a triangle, which has three vertices, we can analyze the situation step by step.

Understanding the Structure of a Triangle

A triangle consists of three vertices, which we can label as A, B, and C. The sides of the triangle are the line segments connecting these vertices: AB, BC, and CA.

Identifying the Vertices

• Vertex A
• Vertex B
• Vertex C

Analyzing Connections

Now, let's consider the connections between these vertices:

• From vertex A, you can connect to B and C (these are the sides).
• From vertex B, you can connect to A and C (again, these are the sides).
• From vertex C, you can connect to A and B (sides once more).

Finding Non-Adjacent Vertices

In a triangle, every vertex is adjacent to the other two. This means that there are no pairs of vertices that are non-adjacent. Therefore, there are no line segments that can be drawn between non-adjacent vertices.

Conclusion on Diagonals

Since a diagonal must connect non-adjacent vertices and all vertices in a triangle are adjacent, we conclude that a triangle has 0 diagonals.

So, the correct answer to your question is (a) 0. This illustrates an interesting property of triangles compared to polygons with more sides, where diagonals become more prevalent as the number of vertices increases.