Lines & angles
Complementary, supplementary and vertical angle equations, and angles formed by parallel lines and a transversal.
Angle pair equationsHSG.CO.C.9Write and solve an equation for complementary, supplementary and vertical angles whose measures are expressions in x.Parallel lines and transversalsHSG.CO.C.9Use corresponding, alternate interior, alternate exterior and same-side interior angles to find missing angles and solve for x.
Triangles & congruence
The triangle angle sum and exterior angles, the triangle inequality, the midsegment theorem and the SSS, SAS, ASA, AAS and HL congruence rules.
Triangle angle sum and exterior anglesHSG.CO.C.10Use the triangle angle sum (180°) and the exterior angle theorem to find missing angles and solve for x.Triangle inequality theoremDecide whether three lengths can form a triangle, and find the possible lengths of a third side from the other two.Triangle congruence (SSS, SAS, ASA, AAS, HL)HSG.SRT.B.5Match given pairs of equal sides and angles to the SSS, SAS, ASA, AAS and HL congruence rules, and spot SSA and AAA, which prove nothing.Triangle midsegment theoremHSG.CO.C.10Use the midsegment theorem: a segment joining the midpoints of two sides is parallel to the third side and half as long.
Polygons & quadrilaterals
Interior and exterior angles of polygons, properties of parallelograms and the area of regular polygons.
Interior and exterior angles of polygonsFind the sum of the interior angles of a polygon, each interior and exterior angle of a regular polygon, and the number of sides from an angle.Properties of parallelogramsHSG.CO.C.11Use the facts that opposite sides and opposite angles of a parallelogram are equal, and consecutive angles add to 180°, to solve for x.Area of regular polygonsFind the area of a regular polygon from its apothem and perimeter, and the exact area of a regular hexagon from its side.
Similarity
Scale factors of similar triangles, areas of similar figures and the triangle proportionality theorem.
Similar triangles and scale factorsHSG.SRT.B.5Use the scale factor between similar triangles to find a missing side, and the square of the scale factor to compare areas.Triangle proportionality (side splitter)HSG.SRT.B.4A line parallel to one side of a triangle divides the other two sides proportionally; use it to find missing segments and the parallel segment.
Right triangles & trigonometry
Special right triangles, sine, cosine and tangent, solving right triangles, and the laws of sines and cosines.
Special right triangles (45-45-90 and 30-60-90)HSG.SRT.C.6Find missing sides of 45-45-90 and 30-60-90 triangles exactly, using the side ratios 1 : 1 : √2 and 1 : √3 : 2.Trigonometric ratios (sine, cosine, tangent)HSG.SRT.C.6Write the sine, cosine and tangent of an acute angle in a right triangle as fractions, including when one side must first be found.Solving right triangles with trigonometryHSG.SRT.C.8Use sine, cosine and tangent to find a missing side of a right triangle, and inverse trigonometry to find a missing angle.Law of sines and law of cosinesHSG.SRT.D.11Find missing sides and angles of any triangle with the law of sines and the law of cosines.
Circles
Arc length and sector area, inscribed and central angles, chords, secants and tangents, and the equation of a circle.
Arc length and sector areaHSG.C.B.5Find the length of an arc and the area of a sector from the radius and the central angle, and find the central angle from an arc length.Inscribed and central anglesHSG.C.A.2Use the facts that a central angle equals its arc and an inscribed angle is half its arc to find angles, arcs and x.Equation of a circleHSG.GPE.A.1Write the equation of a circle from its center and radius, read the center and radius from standard form, and complete the square to find them from general form.Segments of chords, secants and tangentsHSG.C.A.2Use the intersecting chords theorem and the tangent-secant theorem to find missing segment lengths in circles.
Coordinate geometry
The distance and midpoint formulas and partitioning a segment in a ratio.
Surface area & volume
Surface area of prisms, cylinders, pyramids, cones and spheres, and the volume of pyramids and prisms.
Surface area of prisms, cylinders, cones, pyramids and spheresFind the total surface area of rectangular prisms, cylinders, square pyramids, spheres and cones, including cones where the slant height must be found first.Volume of pyramids and prismsHSG.GMD.A.3Find the volume of triangular prisms and of square and rectangular pyramids, and work backward from a volume to a missing height.