Junior Cert Geometry (First Year)
Axioms and Theorems Familiarity through Discovery and Investigation		O (G)	H (A)
	Axioms
1	There is exactly one line through any two given points [Two Points Axiom].
2	The 4 properties of the distance between points [Ruler Axiom]. (i) The distance |AB| is never negative; (ii) |AB| = |BA|; (iii) if C lies on AB, between A and B, then |AB| = |AC| + |CB|; (iv) Given any ray from A, and given any real number k ≥0, there is a unique point B on the ray whose distance from A is k [Marking off distance].
3	The number of degrees in an angle is always between 0^o and 360^o [Protractor Axiom]. The number of degrees of an ordinary angle is less than 180^o. A straight angle has 180^o.
4	Congruent triangles conditions [SSS, SAS, ASA]. [If these conditions apply then the triangles are congruent].
5	Given any line l and a point P, there is exactly one line through P that is parallel to l [Axiom of Parallels].
	Theorems Linked to dynamic geometry illustrations)
1	Vertically opposite angles are equal in measure [or See In Geogebra file here ]
2	In an isosceles triangle the angles opposite the equal sides are equal And Conversely, if two angles are equal, then the triangle is isosceles.
3	If a transversal makes equal alternate angles on two lines then the lines are parallel And Converse
4	The angles in any triangle add to 180^o
5	Two lines are parallel if, and only if, for any transversal, the corresponding angles are equal
6	Each exterior angle of a triangle is equal to the sum of the interior opposite angles.

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