Which of the following statements is false ?

Options

A. A triangle has three sides
B. A triangle has three vertices
C. A triangle has three angles
D. A triangle has two diagonals

Answer

To determine which statement about triangles is false, we will analyze each statement one by one.

1. **Statement 1**: A triangle has three sides.
- A triangle is defined as a polygon with three sides. If we label the triangle as ABC, the sides are AB, BC, and CA. Therefore, this statement is **true**.

2. **Statement 2**: A triangle has three vertices.
- The vertices of a triangle are the points where the sides meet. In triangle ABC, the vertices are A, B, and C. Thus, this statement is also **true**.

3. **Statement 3**: A triangle has three angles.
- A triangle consists of three angles formed by its sides. In triangle ABC, the angles are ∠CAB, ∠ABC, and ∠BCA. Hence, this statement is **true**.

4. **Statement 4**: A triangle has two diagonals.
- A diagonal is a line segment connecting two non-adjacent vertices of a polygon. In a triangle, there are no non-adjacent vertices, as each vertex is adjacent to the other two. Therefore, a triangle has **zero diagonals**, making this statement **false**.

Based on our analysis, the false statement is: **A triangle has two diagonals.**