### Axioms

**Axiom**: A statement or proposition that is regarded as being established, accepted, or self-evidently true.

**Axiom 1**: There is exactly one line through any two given points**Axiom 2**: [Ruler Axiom]: The properties of the distance between points.**Axiom 3**: Protractor Axiom (The properties of the degree measure of an angle).**Axiom 4**: Congruent triangles conditions (SSS, SAS, ASA)**Axiom 5**: Given any line l and a point P, there is exactly one line through P that is parallel to l.

### Corollaries

**Corollary**: A proposition that follows from (and is often appended to) one already proved.

**Corollary 1**. A diagonal divides a parallelogram into two congruent triangles.**Corollary 2**: All angles at points of a circle, standing on the same arc are equal (and converse).**Corollary 3**: Each angle in a semi-circle is a right angle.**Corollary 4**: If the angle standing on a chord [BC] at some point of the circle is a rightangle, then [BC] is a diameter.**Corollary 5**: If ABCD is a cyclic quadrilateral, then opposite angles sum to 180.**Corollary 6**: If two circles intersect at one point only, then the two centres and the point of contact are collinear.

### Theorems

**Theorem**: A general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths.