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
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
chords and their properties
tangent lines
inscribed/circumscribed triangles, quadrilaterals
construction problems based on all of the above