IXL Skill Plan | Kentucky Academic Standards: Geometry

Kentucky Academic Standards: Geometry

Skills available for Kentucky Geometry standards

Domain

Number and Quantity
Geometry

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N	Number and Quantity
Quantities
Reason quantitatively and use units to solve problems.
Reason quantitatively and use units to solve problems.

KY.HS.N.5: Define appropriate units in context for the purpose of descriptive modeling.		1. Scale drawings: word problems
KY.HS.N.5: Define appropriate units in context for the purpose of descriptive modeling.
1. Scale drawings: word problems
KY.HS.N.6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.		Precision 1. Precision Greatest possible error 2. Greatest possible error 3. Minimum and maximum area and volume Percent error 4. Percent error 5. Percent error: area and volume
KY.HS.N.6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Precision 1. Precision Greatest possible error 2. Greatest possible error 3. Minimum and maximum area and volume Percent error 4. Percent error 5. Percent error: area and volume

G	Geometry
Congruence
Experiment with transformations in the plane.
Experiment with transformations in the plane.

KY.HS.G.1: Know and apply precise definitions of the language of Geometry:
KY.HS.G.1: Know and apply precise definitions of the language of Geometry:

KY.HS.G.1.a: Understand properties of line segments, angles and circle.		1. Angle vocabulary
KY.HS.G.1.a: Understand properties of line segments, angles and circle.
1. Angle vocabulary
KY.HS.G.1.b: Understand properties of and differences between perpendicular and parallel lines.		1. Identify parallel, intersecting, and skew lines and planes
KY.HS.G.1.b: Understand properties of and differences between perpendicular and parallel lines.
1. Identify parallel, intersecting, and skew lines and planes
KY.HS.G.2: Representing transformations in the plane.
KY.HS.G.2: Representing transformations in the plane.

KY.HS.G.2.a: Describe transformations as functions that take points in the plane as inputs and give other points as outputs.		Translations 1. Translations: graph the image 2. Translations: find the coordinates 3. Translations: write the rule Reflections 4. Reflections: graph the image 5. Reflections: find the coordinates Rotations 6. Rotations: graph the image 7. Rotations: find the coordinates Congruence transformations 8. Classify congruence transformations 9. Sequences of congruence transformations: graph the image 10. Congruence transformations: mixed review Dilations 11. Dilations: graph the image 12. Dilations: find the coordinates 13. Dilations: find the scale factor
KY.HS.G.2.a: Describe transformations as functions that take points in the plane as inputs and give other points as outputs.
Translations 1. Translations: graph the image 2. Translations: find the coordinates 3. Translations: write the rule Reflections 4. Reflections: graph the image 5. Reflections: find the coordinates Rotations 6. Rotations: graph the image 7. Rotations: find the coordinates Congruence transformations 8. Classify congruence transformations 9. Sequences of congruence transformations: graph the image 10. Congruence transformations: mixed review Dilations 11. Dilations: graph the image 12. Dilations: find the coordinates 13. Dilations: find the scale factor
KY.HS.G.2.b: Compare transformations that preserve distance and angle measures to those that do not.
KY.HS.G.2.b: Compare transformations that preserve distance and angle measures to those that do not.

KY.HS.G.2.c: Given a rectangle, parallelogram, trapezoid, or regular polygon, formally describe the rotations and reflections that carry it onto itself, using properties of these figures.		1. Transformations that carry a polygon onto itself
KY.HS.G.2.c: Given a rectangle, parallelogram, trapezoid, or regular polygon, formally describe the rotations and reflections that carry it onto itself, using properties of these figures.
1. Transformations that carry a polygon onto itself
KY.HS.G.4: Understand the effects of transformations of geometric figures.
KY.HS.G.4: Understand the effects of transformations of geometric figures.

KY.HS.G.4.a: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure.		1. Translations: graph the image 2. Reflections: graph the image 3. Rotations: graph the image
KY.HS.G.4.a: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure.
1. Translations: graph the image 2. Reflections: graph the image 3. Rotations: graph the image
KY.HS.G.4.b: Specify a sequence of transformations that will carry a given figure onto another.		1. Sequences of congruence transformations: graph the image 2. Sequences of congruence transformations: find the rules
KY.HS.G.4.b: Specify a sequence of transformations that will carry a given figure onto another.
1. Sequences of congruence transformations: graph the image 2. Sequences of congruence transformations: find the rules
KY.HS.G.4.c: 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.		1. Sequences of congruence transformations: graph the image 2. Sequences of congruence transformations: choose the sequence 3. Transformations that carry a polygon onto itself 4. Congruence transformations: mixed review 5. Determine if two figures are congruent: justify your answer
KY.HS.G.4.c: 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.
1. Sequences of congruence transformations: graph the image 2. Sequences of congruence transformations: choose the sequence 3. Transformations that carry a polygon onto itself 4. Congruence transformations: mixed review 5. Determine if two figures are congruent: justify your answer
Checkpoint opportunity		1. Checkpoint: Definitions of geometric objects 2. Checkpoint: Congruence transformations 3. Checkpoint: Transformations in the plane
Checkpoint opportunity
1. Checkpoint: Definitions of geometric objects 2. Checkpoint: Congruence transformations 3. Checkpoint: Transformations in the plane

Understand congruence in terms of rigid motions.
Understand congruence in terms of rigid motions.

KY.HS.G.5: Know and apply the concepts of triangle congruence:
KY.HS.G.5: Know and apply the concepts of triangle congruence:

KY.HS.G.5.a: 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.		1. Prove triangles are congruent using rigid motions
KY.HS.G.5.a: 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.
1. Prove triangles are congruent using rigid motions
KY.HS.G.5.b: Explain how the criteria for triangle congruence (ASA, SAS and SSS) follow from the definition of congruence in terms of rigid motions.
KY.HS.G.5.b: Explain how the criteria for triangle congruence (ASA, SAS and SSS) follow from the definition of congruence in terms of rigid motions.

Checkpoint opportunity		1. Checkpoint: Rigid motion and congruence
Checkpoint opportunity
1. Checkpoint: Rigid motion and congruence

Prove geometric theorems.
Prove geometric theorems.

KY.HS.G.6: Apply theorems for lines, angles, triangles, parallelograms.		Lines and angles 1. Perpendicular Bisector Theorem 2. Angle diagrams: solve for the variable 3. Angle bisectors 4. Transversals of parallel lines: find angle measures 5. Transversals of parallel lines: solve for x Triangles 6. Triangle Angle-Sum Theorem 7. Congruence statements and corresponding parts 8. Solve problems involving corresponding parts 9. Congruency in isosceles and equilateral triangles 10. Find the centroid of a triangle Parallelograms 11. Properties of parallelograms 12. Proving a quadrilateral is a parallelogram 13. Properties of rhombuses 14. Properties of squares and rectangles
KY.HS.G.6: Apply theorems for lines, angles, triangles, parallelograms.
Lines and angles 1. Perpendicular Bisector Theorem 2. Angle diagrams: solve for the variable 3. Angle bisectors 4. Transversals of parallel lines: find angle measures 5. Transversals of parallel lines: solve for x Triangles 6. Triangle Angle-Sum Theorem 7. Congruence statements and corresponding parts 8. Solve problems involving corresponding parts 9. Congruency in isosceles and equilateral triangles 10. Find the centroid of a triangle Parallelograms 11. Properties of parallelograms 12. Proving a quadrilateral is a parallelogram 13. Properties of rhombuses 14. Properties of squares and rectangles
KY.HS.G.7: Prove theorems about geometric figures.
KY.HS.G.7: Prove theorems about geometric figures.

KY.HS.G.7.a: Construct formal proofs to justify theorems for lines, angles and triangles.		Proofs involving angles 1. Proofs involving angles Proofs involving lines 2. Proofs involving parallel lines I 3. Proofs involving parallel lines II Proofs involving triangles 4. Proving triangles congruent by SSS and SAS 5. Proving triangles congruent by ASA and AAS 6. SSS Theorem in the coordinate plane 7. Proving triangles congruent by SSS, SAS, ASA, and AAS 8. Proofs involving isosceles triangles 9. Hypotenuse-Leg Theorem 10. Proofs involving triangles I 11. Proofs involving triangles II
KY.HS.G.7.a: Construct formal proofs to justify theorems for lines, angles and triangles.
Proofs involving angles 1. Proofs involving angles Proofs involving lines 2. Proofs involving parallel lines I 3. Proofs involving parallel lines II Proofs involving triangles 4. Proving triangles congruent by SSS and SAS 5. Proving triangles congruent by ASA and AAS 6. SSS Theorem in the coordinate plane 7. Proving triangles congruent by SSS, SAS, ASA, and AAS 8. Proofs involving isosceles triangles 9. Hypotenuse-Leg Theorem 10. Proofs involving triangles I 11. Proofs involving triangles II
Checkpoint opportunity		1. Checkpoint: Line and angle theorems 2. Checkpoint: Triangle theorems 3. Checkpoint: Parallelogram theorems
Checkpoint opportunity
1. Checkpoint: Line and angle theorems 2. Checkpoint: Triangle theorems 3. Checkpoint: Parallelogram theorems

Make geometric constructions.
Make geometric constructions.

KY.HS.G.8: Create and apply geometric constructions.
KY.HS.G.8: Create and apply geometric constructions.

KY.HS.G.8.a: Make formal geometric constructions with a variety of tools and methods.		Angles 1. Construct an angle bisector 2. Construct a congruent angle Points, lines, and segments 3. Construct a congruent segment 4. Construct the midpoint or perpendicular bisector of a segment 5. Construct a perpendicular line 6. Construct parallel lines Regular polygons 7. Construct an equilateral triangle or regular hexagon 8. Construct a square Triangles 9. Construct the circumcenter or incenter of a triangle 10. Construct the centroid or orthocenter of a triangle Circles 11. Construct a tangent line to a circle 12. Construct the inscribed or circumscribed circle of a triangle
KY.HS.G.8.a: Make formal geometric constructions with a variety of tools and methods.
Angles 1. Construct an angle bisector 2. Construct a congruent angle Points, lines, and segments 3. Construct a congruent segment 4. Construct the midpoint or perpendicular bisector of a segment 5. Construct a perpendicular line 6. Construct parallel lines Regular polygons 7. Construct an equilateral triangle or regular hexagon 8. Construct a square Triangles 9. Construct the circumcenter or incenter of a triangle 10. Construct the centroid or orthocenter of a triangle Circles 11. Construct a tangent line to a circle 12. Construct the inscribed or circumscribed circle of a triangle
KY.HS.G.8.b: Apply basic construction procedures to construct more complex figures.		1. Construct an equilateral triangle inscribed in a circle 2. Construct a square inscribed in a circle 3. Construct a regular hexagon inscribed in a circle
KY.HS.G.8.b: Apply basic construction procedures to construct more complex figures.
1. Construct an equilateral triangle inscribed in a circle 2. Construct a square inscribed in a circle 3. Construct a regular hexagon inscribed in a circle
Checkpoint opportunity		1. Checkpoint: Geometric constructions
Checkpoint opportunity
1. Checkpoint: Geometric constructions
Similarity, Right Triangles and Trigonometry
Understand similarity in terms of similarity transformations.
Understand similarity in terms of similarity transformations.

KY.HS.G.9: Understand properties of dilations.
KY.HS.G.9: Understand properties of dilations.

KY.HS.G.9.a: Verify the properties that result from that dilations given by a center and a scale factor.		1. Dilations: find length, perimeter, and area 2. Dilations: find the scale factor 3. Dilations: find the scale factor and center of the dilation
KY.HS.G.9.a: Verify the properties that result from that dilations given by a center and a scale factor.
1. Dilations: find length, perimeter, and area 2. Dilations: find the scale factor 3. Dilations: find the scale factor and center of the dilation
KY.HS.G.9.b: Verify that a dilation produces an image that is similar to the pre-image.		Similar figures 1. Ratios in similar figures 2. Identify similar figures 3. Side lengths and angle measures in similar figures Dilations 4. Dilations: graph the image 5. Dilations and parallel lines
KY.HS.G.9.b: Verify that a dilation produces an image that is similar to the pre-image.
Similar figures 1. Ratios in similar figures 2. Identify similar figures 3. Side lengths and angle measures in similar figures Dilations 4. Dilations: graph the image 5. Dilations and parallel lines
KY.HS.G.10: Apply the properties of similarity transformations to establish the AA criterion for two triangles to be similar.		1. Similar triangles and indirect measurement 2. Similarity rules for triangles
KY.HS.G.10: Apply the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
1. Similar triangles and indirect measurement 2. Similarity rules for triangles
Checkpoint opportunity		1. Checkpoint: Dilations 2. Checkpoint: Similarity transformations
Checkpoint opportunity
1. Checkpoint: Dilations 2. Checkpoint: Similarity transformations

Prove theorems involving similarity.
Prove theorems involving similarity.

KY.HS.G.11: Understand theorems about triangles.
KY.HS.G.11: Understand theorems about triangles.

KY.HS.G.11.a: Apply theorems about triangles.		Triangle midsegments 1. Midsegments of triangles Triangle Proportionality Theorem 2. Triangle Proportionality Theorem Pythagorean Theorem 3. Pythagorean theorem 4. Converse of the Pythagorean theorem 5. Pythagorean Inequality Theorems Prove theorems about triangles 6. Proofs involving triangles II
KY.HS.G.11.a: Apply theorems about triangles.
Triangle midsegments 1. Midsegments of triangles Triangle Proportionality Theorem 2. Triangle Proportionality Theorem Pythagorean Theorem 3. Pythagorean theorem 4. Converse of the Pythagorean theorem 5. Pythagorean Inequality Theorems Prove theorems about triangles 6. Proofs involving triangles II
KY.HS.G.11.c: Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures.		Similar triangles 1. Similar triangles and indirect measurement 2. Similarity rules for triangles 3. Triangle Proportionality Theorem 4. Similarity and altitudes in right triangles Proofs involving similar triangles 5. Prove similarity statements 6. Prove proportions or angle congruences using similarity
KY.HS.G.11.c: Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Similar triangles 1. Similar triangles and indirect measurement 2. Similarity rules for triangles 3. Triangle Proportionality Theorem 4. Similarity and altitudes in right triangles Proofs involving similar triangles 5. Prove similarity statements 6. Prove proportions or angle congruences using similarity
Checkpoint opportunity		1. Checkpoint: Triangle similarity and congruence
Checkpoint opportunity
1. Checkpoint: Triangle similarity and congruence

Define trigonometric ratios and solve problems involving right triangles.
Define trigonometric ratios and solve problems involving right triangles.

KY.HS.G.12: Understand properties of right triangles.
KY.HS.G.12: Understand properties of right triangles.

KY.HS.G.12.a: Understand 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 (sine, cosine and tangent).		1. Trigonometric ratios: sin, cos, and tan 2. Trigonometric ratios with radicals: sin, cos, and tan 3. Trigonometric ratios: csc, sec, and cot 4. Trigonometric ratios in similar right triangles
KY.HS.G.12.a: Understand 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 (sine, cosine and tangent).
1. Trigonometric ratios: sin, cos, and tan 2. Trigonometric ratios with radicals: sin, cos, and tan 3. Trigonometric ratios: csc, sec, and cot 4. Trigonometric ratios in similar right triangles
KY.HS.G.12.b: Explain and use the relationship between the sine and cosine of complementary angles.		1. Sine and cosine of complementary angles
KY.HS.G.12.b: Explain and use the relationship between the sine and cosine of complementary angles.
1. Sine and cosine of complementary angles
KY.HS.G.12.c: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.		Pythagorean Theorem 1. Pythagorean theorem 2. Converse of the Pythagorean theorem 3. Pythagorean Inequality Theorems Trigonometric ratios 4. Trigonometric ratios: find a side length 5. Trigonometric ratios: find an angle measure Solve a right triangle 6. Solve a right triangle
KY.HS.G.12.c: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Pythagorean Theorem 1. Pythagorean theorem 2. Converse of the Pythagorean theorem 3. Pythagorean Inequality Theorems Trigonometric ratios 4. Trigonometric ratios: find a side length 5. Trigonometric ratios: find an angle measure Solve a right triangle 6. Solve a right triangle
Checkpoint opportunity		1. Checkpoint: Right triangle trigonometry
Checkpoint opportunity
1. Checkpoint: Right triangle trigonometry
Circles
Understand and apply theorems about circles.
Understand and apply theorems about circles.

KY.HS.G.15: Verify using dilations that all circles are similar.		1. Similarity of circles
KY.HS.G.15: Verify using dilations that all circles are similar.
1. Similarity of circles
KY.HS.G.16: Identify and describe relationships among angles and segments within the context of circles involving:
KY.HS.G.16: Identify and describe relationships among angles and segments within the context of circles involving:

KY.HS.G.16.a: Recognize differences between and properties of inscribed, central and circumscribed angles.		1. Central angles and arc measures 2. Arcs and chords 3. Angles formed by chords, secants, and tangents 4. Segments formed by chords, secants, and tangents
KY.HS.G.16.a: Recognize differences between and properties of inscribed, central and circumscribed angles.
1. Central angles and arc measures 2. Arcs and chords 3. Angles formed by chords, secants, and tangents 4. Segments formed by chords, secants, and tangents
KY.HS.G.16.b: Understand relationships between inscribed angles and the diameter of a circle.		1. Inscribed angles 2. Angles in inscribed right triangles
KY.HS.G.16.b: Understand relationships between inscribed angles and the diameter of a circle.
1. Inscribed angles 2. Angles in inscribed right triangles
KY.HS.G.16.c: Understand the relationship between the radius of a circle and the line drawn through the point of tangency on that radius.		1. Tangent lines
KY.HS.G.16.c: Understand the relationship between the radius of a circle and the line drawn through the point of tangency on that radius.
1. Tangent lines
Checkpoint opportunity		1. Checkpoint: Prove circles are similar 2. Checkpoint: Angles and lines in circles
Checkpoint opportunity
1. Checkpoint: Prove circles are similar 2. Checkpoint: Angles and lines in circles
Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section.
Translate between the geometric description and the equation for a conic section.

KY.HS.G.19: Understand the relationship between the algebraic form and the geometric representation of a circle.
KY.HS.G.19: Understand the relationship between the algebraic form and the geometric representation of a circle.

KY.HS.G.19.a: Write the equation of a circle of given center and radius using the Pythagorean Theorem.		1. Write equations of circles in standard form from graphs 2. Write equations of circles in standard form using properties 3. Graph circles from equations in standard form
KY.HS.G.19.a: Write the equation of a circle of given center and radius using the Pythagorean Theorem.
1. Write equations of circles in standard form from graphs 2. Write equations of circles in standard form using properties 3. Graph circles from equations in standard form
Checkpoint opportunity		1. Checkpoint: Equations of circles
Checkpoint opportunity
1. Checkpoint: Equations of circles

Use coordinates to prove simple geometric theorems algebraically.
Use coordinates to prove simple geometric theorems algebraically.

KY.HS.G.21: Use coordinates to justify and prove simple geometric theorems algebraically.		1. Classify shapes on the coordinate plane: justify your answer 2. Determine if a point lies on a circle
KY.HS.G.21: Use coordinates to justify and prove simple geometric theorems algebraically.
1. Classify shapes on the coordinate plane: justify your answer 2. Determine if a point lies on a circle
KY.HS.G.22: Justify and apply the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.		1. Slopes of parallel and perpendicular lines 2. Equations of parallel and perpendicular lines 3. Find the distance between a point and a line 4. Find the distance between two parallel lines
KY.HS.G.22: Justify and apply the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
1. Slopes of parallel and perpendicular lines 2. Equations of parallel and perpendicular lines 3. Find the distance between a point and a line 4. Find the distance between two parallel lines
KY.HS.G.23: Find measurements among points within the coordinate plane.
KY.HS.G.23: Find measurements among points within the coordinate plane.

KY.HS.G.23.a: Use points from the coordinate plane to find the coordinates of a midpoint of a line segment and the distance between the endpoints of a line segment.		Midpoint 1. Midpoints 2. Midpoint formula: find the midpoint 3. Midpoint formula: find the endpoint Distance 4. Distance formula
KY.HS.G.23.a: Use points from the coordinate plane to find the coordinates of a midpoint of a line segment and the distance between the endpoints of a line segment.
Midpoint 1. Midpoints 2. Midpoint formula: find the midpoint 3. Midpoint formula: find the endpoint Distance 4. Distance formula
KY.HS.G.23.b: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.		1. Partition a line segment in a given ratio
KY.HS.G.23.b: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
1. Partition a line segment in a given ratio
KY.HS.G.24: Use coordinates within the coordinate plane to calculate measurements of two dimensional figures.
KY.HS.G.24: Use coordinates within the coordinate plane to calculate measurements of two dimensional figures.

KY.HS.G.24.a: Compute the perimeters of various polygons.		1. Area and perimeter in the coordinate plane I 2. Area and perimeter in the coordinate plane II
KY.HS.G.24.a: Compute the perimeters of various polygons.
1. Area and perimeter in the coordinate plane I 2. Area and perimeter in the coordinate plane II
KY.HS.G.24.b: Compute the areas of triangles, rectangles and other quadrilaterals.		1. Area and perimeter in the coordinate plane I 2. Area and perimeter in the coordinate plane II
KY.HS.G.24.b: Compute the areas of triangles, rectangles and other quadrilaterals.
1. Area and perimeter in the coordinate plane I 2. Area and perimeter in the coordinate plane II
Checkpoint opportunity		1. Checkpoint: Partition a line segment 2. Checkpoint: Coordinate proofs 3. Checkpoint: Parallel and perpendicular lines 4. Checkpoint: Area and perimeter in the coordinate plane
Checkpoint opportunity
1. Checkpoint: Partition a line segment 2. Checkpoint: Coordinate proofs 3. Checkpoint: Parallel and perpendicular lines 4. Checkpoint: Area and perimeter in the coordinate plane
Geometric Measurement and Dimensions
Explain volume formulas and use them to solve problems.
Explain volume formulas and use them to solve problems.

KY.HS.G.25: Analyze and determine the validity of arguments for the formulas for the various figures and shapes.
KY.HS.G.25: Analyze and determine the validity of arguments for the formulas for the various figures and shapes.

KY.HS.G.25.a: Finding the circumference and area of a circle.		1. Area and circumference of circles
KY.HS.G.25.a: Finding the circumference and area of a circle.
1. Area and circumference of circles
KY.HS.G.25.b: Finding the volume of a sphere, prism, cylinder, pyramid and cone.		1. Volume of prisms and cylinders 2. Volume of pyramids and cones 3. Volume of spheres
KY.HS.G.25.b: Finding the volume of a sphere, prism, cylinder, pyramid and cone.
1. Volume of prisms and cylinders 2. Volume of pyramids and cones 3. Volume of spheres
KY.HS.G.27: Use volume formulas to solve problems for cylinders, pyramids, cones, spheres, prisms.		1. Volume of prisms and cylinders 2. Volume of pyramids and cones 3. Volume of spheres
KY.HS.G.27: Use volume formulas to solve problems for cylinders, pyramids, cones, spheres, prisms.
1. Volume of prisms and cylinders 2. Volume of pyramids and cones 3. Volume of spheres
Checkpoint opportunity		1. Checkpoint: Volume
Checkpoint opportunity
1. Checkpoint: Volume

Visualize relationships between two-dimensional and three-dimensional objects.
Visualize relationships between two-dimensional and three-dimensional objects.

KY.HS.G.28: Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects.		1. Cross sections of three-dimensional figures 2. Solids of revolution
KY.HS.G.28: Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects.
1. Cross sections of three-dimensional figures 2. Solids of revolution
Checkpoint opportunity		1. Checkpoint: Cross sections and solids of revolution
Checkpoint opportunity
1. Checkpoint: Cross sections and solids of revolution
Modeling with Geometry
Apply geometric concepts in modeling situations.
Apply geometric concepts in modeling situations.

KY.HS.G.29: Use geometric shapes, their measures and their properties to describe objects in real world settings.		1. Pythagorean theorem
KY.HS.G.29: Use geometric shapes, their measures and their properties to describe objects in real world settings.
1. Pythagorean theorem
KY.HS.G.30: Apply concepts of density based on area and volume in modeling situations, using appropriate units of measurement.		1. Calculate density, mass, and volume
KY.HS.G.30: Apply concepts of density based on area and volume in modeling situations, using appropriate units of measurement.
1. Calculate density, mass, and volume
KY.HS.G.31: Apply geometric methods to solve design problems.
KY.HS.G.31: Apply geometric methods to solve design problems.

Checkpoint opportunity		1. Checkpoint: Geometric modeling and design 2. Checkpoint: Density
Checkpoint opportunity
1. Checkpoint: Geometric modeling and design 2. Checkpoint: Density