Assumptions in geometry that have no proof and are universally accepted are called "axioms".

Definition of Axioms:
Axioms are statements that are assumed to be true without proof. They serve as the foundation of a logical system, providing the starting point for all further deductions and proofs. Axioms are universally accepted and are considered to be self-evident truths. In geometry, axioms are used to establish the basic properties and relationships of geometric figures and space.

Key Points:
- Assumptions in geometry that have no proof are called axioms.
- Axioms are universally accepted and considered to be self-evident truths.
- Axioms serve as the foundation of a logical system in geometry.
- Axioms are used to establish the basic properties and relationships of geometric figures and space.

Importance of Axioms:
Axioms play a crucial role in geometry as they provide a starting point for logical reasoning. They are the building blocks upon which all further deductions and proofs are based. Without axioms, it would be impossible to establish the fundamental principles and properties of geometry.

Examples of Axioms in Geometry:
1. The shortest distance between two points is a straight line.
2. Two parallel lines never intersect.
3. If two angles are congruent and a third angle is congruent to one of them, then the third angle is congruent to the other angle.
4. If two triangles are congruent to a third triangle, then they are congruent to each other.

Conclusion:
In geometry, axioms are assumptions that are universally accepted and have no proof. They serve as the foundation of logical reasoning and are used to establish the basic properties and relationships of geometric figures and space. Axioms are essential in geometry as they provide a starting point for further deductions and proofs.