State True or False
If two adjacent sides of a parallelogram are equal, it is a rhombus

Answer

To determine whether the statement "If two adjacent sides of a parallelogram are equal, it is a rhombus" is true or false, we can analyze the properties of parallelograms and rhombuses step by step.

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- A **parallelogram** is a quadrilateral with opposite sides that are both parallel and equal in length.
- A **rhombus** is a special type of parallelogram where all four sides are equal in length.

2. **Identifying Adjacent Sides**:
- In a parallelogram, adjacent sides are the sides that meet at a vertex. For example, if we consider a parallelogram ABCD, the sides AB and AD are adjacent.

3. **Given Condition**:
- The statement mentions that two adjacent sides of the parallelogram are equal. Let's say AB = AD.

4. **Analyzing the Consequences**:
- If AB = AD, then we can also conclude that the opposite sides of the parallelogram must be equal (by the properties of parallelograms). Therefore, BC = AD (since AD is equal to AB).

5. **Establishing Equality of All Sides**:
- Since AB = AD and BC = AD, we can conclude that AB = BC. Thus, all four sides of the parallelogram are equal (AB = AD = BC = CD).

6. **Conclusion**:
- Since all sides of the parallelogram are equal, it meets the definition of a rhombus. Therefore, the statement is **True**.

### Final Answer:
**True**: If two adjacent sides of a parallelogram are equal, it is a rhombus.