Idaho Content Standards (adopted in 2022): Geometry
Skills available for Idaho Geometry standards
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G
Geometry
G.CO Congruence
G.CO.A Experiment with transformations in the plane.
G.CO.A Experiment with transformations in the plane.
G.CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.CO.A.2: Represent transformations in the plane and describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not.
Translations
Reflections
Rotations
Congruence transformations
Dilations
G.CO.A.2: Represent transformations in the plane and describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not.
Translations
Reflections
Rotations
Congruence transformations
Dilations
G.CO.A.3: Describe the rotations and reflections that carry a given figure (rectangle, parallelogram, trapezoid, or regular polygon) onto itself.
G.CO.A.3: Describe the rotations and reflections that carry a given figure (rectangle, parallelogram, trapezoid, or regular polygon) onto itself.
G.CO.A.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.A.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.A.5: Draw the transformation (rotation, reflection, or translation) for a given geometric figure.
G.CO.A.5: Draw the transformation (rotation, reflection, or translation) for a given geometric figure.
G.CO.A.6: Specify a sequence of transformations that will carry a given figure onto another.
G.CO.A.6: Specify a sequence of transformations that will carry a given figure onto another.
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G.CO.B Understand congruence in terms of rigid motions.
G.CO.B Understand congruence in terms of rigid motions.
G.CO.B.7: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
G.CO.B.7: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
G.CO.B.8: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.B.8: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.B.9: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
G.CO.B.9: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
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G.CO.C Prove geometric theorems and, when appropriate, the converse of theorems.
G.CO.C Prove geometric theorems and, when appropriate, the converse of theorems.
G.CO.C.10: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent, and conversely prove lines are parallel; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Angles
Parallel lines
Perpendicular bisectors
G.CO.C.10: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent, and conversely prove lines are parallel; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Angles
Parallel lines
Perpendicular bisectors
G.CO.C.11: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180° base angles of isosceles triangles are congruent, and conversely prove a triangle is isosceles; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Isosceles triangles
Angles in triangles
Segments in triangles
Centroids or orthocenters of triangles
G.CO.C.11: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180° base angles of isosceles triangles are congruent, and conversely prove a triangle is isosceles; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Isosceles triangles
Angles in triangles
Segments in triangles
Centroids or orthocenters of triangles
G.CO.C.12: Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
G.CO.C.12: Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
G.CO.C.12.a: Prove theorems about polygons. Theorems include: the measures of interior and exterior angles; apply properties of polygons to the solutions of mathematical and contextual problems.
Polygons
Quadrilaterals
G.CO.C.12.a: Prove theorems about polygons. Theorems include: the measures of interior and exterior angles; apply properties of polygons to the solutions of mathematical and contextual problems.
Polygons
Quadrilaterals
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G.CO.D Make geometric constructions.
G.CO.D Make geometric constructions.
G.CO.D.13: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.) Constructions include: copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Angles
Points, lines, and segments
Regular polygons
Triangles
Circles
G.CO.D.13: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.) Constructions include: copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Angles
Points, lines, and segments
Regular polygons
Triangles
Circles
G.CO.D.14: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
G.CO.D.14: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
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G.SRT Similarity, Right Triangles, and Trigonometry
G.SRT.A Understand similarity in terms of similarity transformations.
G.SRT.A Understand similarity in terms of similarity transformations.
G.SRT.A.1: Verify experimentally the properties of dilations given by a center and a scale factor.
G.SRT.A.1: Verify experimentally the properties of dilations given by a center and a scale factor.
G.SRT.A.1.a: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
G.SRT.A.1.a: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
G.SRT.A.1.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G.SRT.A.1.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G.SRT.A.2: Use the definition of similarity to decide if two given figures are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G.SRT.A.2: Use the definition of similarity to decide if two given figures are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G.SRT.A.3: Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.
G.SRT.A.3: Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.
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G.SRT.B Prove theorems involving similarity.
G.SRT.B Prove theorems involving similarity.
G.SRT.B.4: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
G.SRT.B.4: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
G.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Congruent triangles
Proofs involving congruent triangles
Isosceles, equilateral, and right triangles
Similar triangles
Proofs involving similar triangles
G.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Congruent triangles
Proofs involving congruent triangles
Isosceles, equilateral, and right triangles
Similar triangles
Proofs involving similar triangles
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G.SRT.C Define trigonometric ratios and solve problems involving right triangles.
G.SRT.C Define trigonometric ratios and solve problems involving right triangles.
G.SRT.C.6: Demonstrate understanding that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
G.SRT.C.6: Demonstrate understanding that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
G.SRT.C.7: Explain and use the relationship between the sine and cosine of complementary angles.
G.SRT.C.7: Explain and use the relationship between the sine and cosine of complementary angles.
G.SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Pythagorean Theorem
Trigonometric ratios
Solve a right triangle
G.SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Pythagorean Theorem
Trigonometric ratios
Solve a right triangle
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G.SRT.D Apply trigonometry to general triangles.
G.SRT.D Apply trigonometry to general triangles.
G.SRT.D.9: (+) Derive the formula A = ½ absin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
G.SRT.D.9: (+) Derive the formula A = ½ absin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
G.SRT.D.10: (+) Prove the Laws of Sines and Cosines and use them to solve problems.
G.SRT.D.10: (+) Prove the Laws of Sines and Cosines and use them to solve problems.
G.SRT.D.11: (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems; resultant forces).
G.SRT.D.11: (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems; resultant forces).
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G.C Circles
G.C.A Understand and apply theorems about circles.
G.C.A Understand and apply theorems about circles.
G.C.A.1: Prove that all circles are similar.
G.C.A.1: Prove that all circles are similar.
G.C.A.2: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
Central and inscribed angles
Chords, secants, and tangents
G.C.A.2: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
Central and inscribed angles
Chords, secants, and tangents
G.C.A.3: Prove properties of angles for a quadrilateral and other polygons inscribed in a circle, by constructing the inscribed and circumscribed circles of a triangle.
Constructions
Properties of angles
G.C.A.3: Prove properties of angles for a quadrilateral and other polygons inscribed in a circle, by constructing the inscribed and circumscribed circles of a triangle.
Constructions
Properties of angles
G.C.A.4: (+) Construct a tangent line to a circle from a point outside the given circle.
G.C.A.4: (+) Construct a tangent line to a circle from a point outside the given circle.
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G.C.B Find arc lengths and areas of sectors of circles.
G.C.B Find arc lengths and areas of sectors of circles.
G.C.B.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
G.C.B.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
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G.GPE Expressing Geometric Properties with Equations
G.GPE.A Translate between the geometric description and the equation for a conic section.
G.GPE.A Translate between the geometric description and the equation for a conic section.
G.GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Complete the square
Write equations and graph circles
G.GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Complete the square
Write equations and graph circles
G.GPE.A.2: Derive the equation of a parabola given a focus and directrix.
Find properties
Write equations
Graph parabolas
G.GPE.A.2: Derive the equation of a parabola given a focus and directrix.
Find properties
Write equations
Graph parabolas
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G.GPE.B Use coordinates to prove simple geometric theorems algebraically.
G.GPE.B Use coordinates to prove simple geometric theorems algebraically.
G.GPE.B.4: Use coordinates to prove simple geometric theorems algebraically, including the distance formula and its relationship to the Pythagorean Theorem.
G.GPE.B.4: Use coordinates to prove simple geometric theorems algebraically, including the distance formula and its relationship to the Pythagorean Theorem.
G.GPE.B.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
G.GPE.B.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
G.GPE.B.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
G.GPE.B.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
G.GPE.B.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles (e.g., using the distance formula).
G.GPE.B.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles (e.g., using the distance formula).
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G.GMD Geometric Measurement and Dimension
G.GMD.A Explain volume formulas and use them to solve problems.
G.GMD.A Explain volume formulas and use them to solve problems.
G.GMD.A.1: Give an informal argument for the formulas for the circumference of a circle; area of a circle; volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.
G.GMD.A.1: Give an informal argument for the formulas for the circumference of a circle; area of a circle; volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.
G.GMD.A.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
G.GMD.A.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
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G.GMD.B Visualize relationships between two-dimensional and three-dimensional objects.
G.GMD.B Visualize relationships between two-dimensional and three-dimensional objects.
G.GMD.B.4: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
G.GMD.B.4: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
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G.MG Modeling with Geometry
G.MG.A Apply geometric concepts in modeling situations.
G.MG.A Apply geometric concepts in modeling situations.
G.MG.A.1: Use geometric shapes, their measures, and their properties to describe objects.
G.MG.A.1: Use geometric shapes, their measures, and their properties to describe objects.
G.MG.A.2: Apply concepts of density based on area and volume in modeling situations.
G.MG.A.2: Apply concepts of density based on area and volume in modeling situations.
G.MG.A.3: Apply geometric methods to solve design problems.
G.MG.A.3: Apply geometric methods to solve design problems.
G.MG.A.4: Use dimensional analysis for unit conversions to confirm that expressions and equations make sense.
G.MG.A.4: Use dimensional analysis for unit conversions to confirm that expressions and equations make sense.
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S
Statistics and probability
S.CP Conditional Probability and the Rules of Probability
S.CP.A Understand independence and conditional probability and use them to interpret data from simulations or experiments.
S.CP.A Understand independence and conditional probability and use them to interpret data from simulations or experiments.
S.CP.A.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
S.CP.A.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
S.CP.A.2: Demonstrate understanding that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
S.CP.A.2: Demonstrate understanding that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
S.CP.A.3: Understand the conditional probability of A given B as as the probability of A and B divided by the probability of B, and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
S.CP.A.3: Understand the conditional probability of A given B as as the probability of A and B divided by the probability of B, and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
S.CP.A.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
S.CP.A.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
S.CP.A.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
S.CP.A.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
S.CP.B Use the rules of probability to compute probabilities of compound events in a uniform probability model.
S.CP.B Use the rules of probability to compute probabilities of compound events in a uniform probability model.
S.CP.B.6: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
S.CP.B.6: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
S.CP.B.7: Apply the Addition Rule, P(A union B) = P(A) + P(B) − P(A intersection B), and interpret the answer in terms of the model.
S.CP.B.7: Apply the Addition Rule, P(A union B) = P(A) + P(B) − P(A intersection B), and interpret the answer in terms of the model.
S.CP.B.8: (+) Apply the general Multiplication Rule in a uniform probability model P(A intersection B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
S.CP.B.8: (+) Apply the general Multiplication Rule in a uniform probability model P(A intersection B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
S.CP.B.9: (+) Use permutations and combinations to compute probabilities of compound events and solve problems.
S.CP.B.9: (+) Use permutations and combinations to compute probabilities of compound events and solve problems.
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S.MD Using Probability to Make Decisions
S.MD.B Use probability to evaluate outcomes of decisions.
S.MD.B Use probability to evaluate outcomes of decisions.
S.MD.B.6: Use probabilities to make objective decisions.
S.MD.B.6: Use probabilities to make objective decisions.
S.MD.B.7: Analyze decisions and strategies using probability concepts.
S.MD.B.7: Analyze decisions and strategies using probability concepts.