Axioms, Corollaries & Theorems

Axioms, Corollaries & Theorems

Axioms

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

  1. Axiom 1: There is exactly one line through any two given points
  2. Axiom 2: [Ruler Axiom]: The properties of the distance between points.
  3. Axiom 3: Protractor Axiom (The properties of the degree measure of an angle).
  4. Axiom 4: Congruent triangles conditions (SSS, SAS, ASA)
  5. 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.

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

View Theorems →

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