Congruent plane figures, superimposition proofs of congruence,
plane isometries (superimposing the plane onto itself), symmetries

Congruent segments and angles; addition/subtraction of segments and angles; 
supplementary angles, vertical angles

broken lines, polygons, triangles

axiom: there is a unique line thru any two distinct points; corollaries

existence and uniqueness of a perpendicular to a given line thru a given point

isosceles triangle, properties

congruence tests for triangles

exterior angles; inequalities between angles and sides in a triangles 
(the greater side is opposite the greater angle, etc)

the triangle inequality, its generalization to broken lines, other applications

right triangles; theorems on lengths of perpendicular and slants 

segment and angle bisectors as geometric loci; all three perp bisectors 
in a triangle intresect at one point, and similarly for angle bisectors

tests for parallel lines (corresponding angles etc)

the parallel postulate, corollaries 

sum of angles in a triangle, in convex polygons

parallelograms, rectangles, rhombi, trapezoids, their properties
and testing for them

circles

central and inscribed angles, arcs

chords and their properties

tangent lines

inscribed/circumscribed triangles

construction problems based on all of the above