Geometry (Iowa Core)

Geometry (G)

• G.G-CO.A.1 Know precise definitions of angle, circle, perpendicular and parallel lines and line segment from undefined terms.
• G.G-CO.A.2 Show transformations with geometry software as functions on points and compare those that keep distance and angle with those that do not.
• G.G-CO.A.3 Describe the rotations and reflections that carry a rectangle, parallelogram, trapezoid or regular polygon onto itself.
• G.G-CO.A.4 Define rotations, reflections and translations using angles, circles, perpendicular and parallel lines and segments.
• G.G-CO.A.5 Draw the image of a figure under a rotation, reflection or translation and give a sequence that maps one figure onto another.
• G.G-CO.B.6 Use rigid motions to transform figures, predict their effect and decide whether two figures are congruent.
• G.G-CO.B.7 Use rigid motions to show triangles are congruent exactly when corresponding sides and angles are congruent.
• G.G-CO.B.8 Explain how ASA, SAS and SSS follow from congruence defined by rigid motions.
• G.G-CO.C.9 Prove theorems about lines and angles, e.g. vertical angles and angles formed by a transversal of parallel lines.
• G.G-CO.C.10 Prove theorems about triangles, e.g. angle sum, isosceles base angles, midsegments and medians.
• G.G-CO.C.11 Prove theorems about parallelograms, e.g. opposite sides and angles, diagonals, and rectangles' diagonals.
• G.G-CO.D.12 Make formal constructions with tools such as compass and straightedge or software: copy, bisect, perpendiculars and parallels.
• G.G-CO.D.13 Construct an equilateral triangle, square and regular hexagon inside a circle.
• G.G-SRT.A.1 Check by experiment the properties of dilations given by a center and scale factor (parts a–b).
• G.G-SRT.A.2 Use similarity transformations to decide if figures are similar and explain similarity of triangles.
• G.G-SRT.A.3 Use properties of similarity transformations to establish the AA criterion for similar triangles.
• G.G-SRT.B.4 Prove theorems about triangles, e.g. the side-splitter theorem and the Pythagorean theorem by similarity.
• G.G-SRT.B.5 Use congruence and similarity criteria to solve problems and prove relationships in figures.
• G.G-SRT.C.6 Define the trigonometric ratios from ratios of sides in similar right triangles.
• G.G-SRT.C.7 Explain and use how the sine and cosine of complementary angles relate.
• G.G-SRT.C.8 Solve right triangles in applied problems with trig ratios and the Pythagorean theorem, including special right triangles.
• G.G-C.A.1 Prove that all circles are similar.
• G.G-C.A.2 Identify and describe relationships among inscribed angles, radii and chords, including central, inscribed and circumscribed angles.
• G.G-C.A.3 Construct inscribed and circumscribed circles of a triangle with technology and explore quadrilaterals inscribed in a circle.
• G.G-C.B.5 Use similarity to show arc length is proportional to radius, define radian measure and derive the sector area formula.
• G.G-GPE.A.1 Derive the equation of a circle from its center and radius and complete the square to find center and radius.
• G.G-GPE.B.4 Use coordinates to prove simple geometric theorems, e.g. whether four points form a rectangle.
• G.G-GPE.B.5 Prove the slope tests for parallel and perpendicular lines and apply them.
• G.G-GPE.B.6 Find the point that divides a directed segment in a given ratio.
• G.G-GPE.B.7 Use coordinates to find perimeters of polygons and areas of triangles and rectangles.
• G.G-GMD.A.1 Give informal arguments for circle circumference and area and the volumes of cylinders, pyramids and cones.
• G.G-GMD.A.3 Solve problems with the volume formulas for cylinders, pyramids, cones and spheres.
• G.G-GMD.B.4 Identify 2D cross-sections of 3D objects and 3D objects made by rotating 2D shapes.
• G.G-MG.A.1 Use shapes, their measures and properties to describe real objects, e.g. a tree trunk as a cylinder.
• G.G-MG.A.2 Use density based on area and volume in modeling, e.g. people per square mile.
• G.G-MG.A.3 Use geometric methods to solve design problems, e.g. meeting physical constraints or keeping costs low.

Statistics and Probability (S)

• G.S-CP.A.1 Describe events as parts of a sample space or as unions, intersections or complements of events.
• G.S-CP.A.2 Understand that A and B are independent when the probability of both is the product of their probabilities, and use this.
• G.S-CP.A.3 Understand conditional probability of A given B and interpret independence in terms of it.
• G.S-CP.A.4 Build and interpret two-way frequency tables and use them to judge independence and estimate conditional probabilities.
• G.S-CP.A.5 Explain conditional probability and independence in everyday language and situations.
• G.S-CP.B.6 Find P(A given B) as the fraction of B's outcomes that are also in A and interpret it.
• G.S-CP.B.7 Apply the addition rule for A or B (add both, subtract the overlap) and interpret it.
• G.S-MD.B.7 Analyze decisions and strategies using probability, e.g. product or medical testing.