High School Geometry (Wisconsin Standards)

Congruence (G.CO)

• M.G.CO.A.1 Know precise definitions of angle, circle, perpendicular and parallel lines and segment.
• M.G.CO.A.2 Represent transformations as functions of points and compare rigid motions with other transformations.
• M.G.CO.A.3 Describe rotations and reflections that map a rectangle, parallelogram, trapezoid or regular polygon onto itself.
• M.G.CO.A.4 Develop definitions of rotations, reflections and translations.
• M.G.CO.A.5 Draw transformed figures and specify a sequence of transformations mapping one figure onto another.
• M.G.CO.B.6 Use rigid motions to transform figures, predict effects and decide congruence.
• M.G.CO.B.7 Show triangles are congruent exactly when corresponding sides and angles are congruent.
• M.G.CO.B.8 Explain how ASA, SAS and SSS follow from congruence defined by rigid motions.
• M.G.CO.C.9 Prove theorems about lines and angles, such as vertical angles and transversals of parallel lines.
• M.G.CO.C.10 Prove theorems about triangles, such as angle sum, isosceles base angles, midsegments and medians.
• M.G.CO.C.11 Prove theorems about parallelograms' sides, angles and diagonals.
• M.G.CO.D.12 Do formal geometric constructions with many tools and methods.
• M.G.CO.D.13 Construct an equilateral triangle, square and regular hexagon inside a circle.

Similarity, Right Triangles, and Trigonometry (G.SRT)

• M.G.SRT.A.1 Verify by experiment the properties of dilations.
  • a. A dilation maps a line to a parallel line.
  • b. A dilation scales segment lengths by the scale factor.
• M.G.SRT.A.2 Use similarity transformations to decide if figures are similar and explain triangle similarity.
• M.G.SRT.A.3 Use similarity transformations to establish the AA criterion.
• M.G.SRT.B.4 Prove theorems about triangles, including proportional sides and the Pythagorean Theorem by similarity.
• M.G.SRT.B.5 Use congruence and similarity criteria to solve problems and prove relationships.
• M.G.SRT.C.6 Understand that right-triangle side ratios depend on the angles, defining trig ratios.
• M.G.SRT.C.7 Explain and use the relationship between sine and cosine of complementary angles.
• M.G.SRT.C.8 Solve right triangles in applied problems with trig ratios and the Pythagorean Theorem.
• M.G.SRT.D.9 Derive the triangle area formula one-half ab sin C.
• M.G.SRT.D.10 Prove the sine and cosine laws and apply them.
• M.G.SRT.D.11 Use the Laws of Sines and Cosines to find unknowns in right and non-right triangles.

Circles (G.C)

• M.G.C.A.1 Describe how inscribed angles, radii and chords relate and prove angle facts for quadrilaterals inscribed in circles.
• M.G.C.B.2 Derive by similarity that arc length is proportional to radius, define radians and find sector areas.

Expressing Geometric Properties with Equations (G.GPE)

• M.G.GPE.A.1 Derive the equation of a circle and complete the square to find its center and radius.
• M.G.GPE.A.2 Derive the equation of a parabola from its focus and directrix.
• M.G.GPE.A.3 Derive equations of ellipses and hyperbolas from their foci.
• M.G.GPE.B.4 Prove simple geometric theorems algebraically with coordinates.
• M.G.GPE.B.5 Prove and use the slope conditions for parallel and perpendicular lines.
• M.G.GPE.B.6 Find the point that divides a directed segment in a given ratio.
• M.G.GPE.B.7 Find polygon perimeters and triangle and rectangle areas from coordinates.

Geometric Measurement and Dimension (G.GMD)

• M.G.GMD.A.1 Give informal arguments for circumference, circle area and cylinder, pyramid and cone volume formulas.
• M.G.GMD.A.2 Find volumes of cylinders, pyramids, cones and spheres with formulas to solve problems.
• M.G.GMD.B.3 Identify 3D objects made by rotating 2D objects.
• M.G.GMD.C.4 Use shapes, their measures and properties to describe real objects, e.g. a tree trunk as a cylinder.
• M.G.GMD.C.5 Use density by area or volume in modeling, e.g. people per square mile.
• M.G.GMD.C.6 Use geometric methods to solve design problems, such as meeting constraints or minimizing cost.