Geometry

From noticing patterns to proving facts: conjectures, if-then statements, and your first two-column proofs.

Transversals and the angle pairs they create — which are congruent, which are supplementary — and proving lines parallel.

Triangle types, the angle sum, the triangle inequality, and the congruence shortcuts SSS · SAS · ASA · AAS · HL.

Bisectors, medians, altitudes, the midsegment theorem, and inequalities inside a triangle.

Angle sums for any polygon; parallelograms, rectangles, rhombi, squares, trapezoids, and kites — with proofs.

Ratio and proportion, similar polygons, the AA · SSS · SAS similarity shortcuts, and the side-splitter theorem.

The Pythagorean theorem, special right triangles, and sine · cosine · tangent with elevation and depression.

Radius, chord, tangent, secant; central and inscribed angles; arcs; and the circle relationships.

Areas of triangles, quadrilaterals and regular polygons; circumference, circle area, sectors, and composite figures.

Prisms, cylinders, pyramids, cones, and spheres — wrapping and filling 3-D solids.

Translations, reflections, rotations, and dilations; symmetry; congruence and similarity re-seen through motion.

Distance, midpoint, and slope; equations of lines and circles; proofs with coordinates — the course capstone.