a common notion
When you tidy a balance scale and add the same weight to both pans, you take for granted that the pans stay balanced. That kind of general, almost self-evident truth — not specific to geometry but to quantity and equality in general — is what Euclid called a common notion.
Euclid distinguished two sorts of starting assumptions. The postulates are about geometric construction (drawing lines and circles). The common notions are broader logical or arithmetical truths used throughout. His five are usually given as: (1) things equal to the same thing are equal to each other; (2) if equals are added to equals, the wholes are equal; (3) if equals are subtracted from equals, the remainders are equal; (4) things that coincide with one another are equal; (5) the whole is greater than the part. These are the engine of equation-handling inside a proof.
In modern usage the line between 'postulate', 'axiom', and 'common notion' has blurred — today we usually call all unproved starting assumptions axioms. The common notions matter because they license the everyday algebraic moves in a geometric proof: when you write 'add AB to both sides' or 'since AB = CD and CD = EF, therefore AB = EF', you are invoking common notion 2 and common notion 1. They are assumed, not proved — that is exactly what makes them notions we hold in common rather than theorems we derive.
In a proof you know AB = CD. You add the same segment, DE, conceptually to each: by common notion 2, AB + (the matched piece) equals CD + (the matched piece). This is the silent justification behind almost every step that combines equal lengths or angles.
Common notions justify the equality-juggling that postulates do not cover.
Postulates are geometric (about drawing), common notions are general (about equality and quantity); modern texts often lump both under the single word 'axiom'.