IXL Skill Plan | Oregon Mathematics Standards: Geometry

Oregon Mathematics Standards: Geometry

Skills available for Oregon Geometry standards

Section

Geometric Reasoning and Measurement

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HS.GM	Geometric Reasoning and Measurement
HS.GM.A Apply geometric transformations to figures through analysis of graphs and understanding of functions.
HS.GM.A.1 Apply definitions of rotations, reflections, and translations to transform a figure and map between two congruent figures in authentic contexts.		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 Mixed congruence transformations 8. Classify congruence transformations 9. Glide reflections: graph the image 10. Sequences of congruence transformations: graph the image 11. Sequences of congruence transformations: find the rules 12. Congruence transformations: mixed review 13. Determine if two figures are congruent: justify your answer 14. Prove triangles are congruent using rigid motions
HS.GM.A.1 Apply definitions of rotations, reflections, and translations to transform a figure and map between two congruent figures in authentic contexts.
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 Mixed congruence transformations 8. Classify congruence transformations 9. Glide reflections: graph the image 10. Sequences of congruence transformations: graph the image 11. Sequences of congruence transformations: find the rules 12. Congruence transformations: mixed review 13. Determine if two figures are congruent: justify your answer 14. Prove triangles are congruent using rigid motions

HS.GM.A.2 Verify experimentally the properties of a dilation given a center and a scale factor. Solve problems in authentic contexts involving similar triangles or dilations.		Dilations 1. Dilations: graph the image 2. Dilations: find the coordinates 3. Dilations: find the scale factor 4. Dilations and parallel lines Similar triangles 5. Similar triangles and similarity transformations
HS.GM.A.2 Verify experimentally the properties of a dilation given a center and a scale factor. Solve problems in authentic contexts involving similar triangles or dilations.
Dilations 1. Dilations: graph the image 2. Dilations: find the coordinates 3. Dilations: find the scale factor 4. Dilations and parallel lines Similar triangles 5. Similar triangles and similarity transformations

HS.GM.A.3 Use the slopes of segments and the coordinates of the vertices of triangles, parallelograms, and trapezoids to solve problems in authentic contexts.		1. Classify triangles 2. Classify quadrilaterals I 3. Classify quadrilaterals II 4. Classify shapes on the coordinate plane: justify your answer
HS.GM.A.3 Use the slopes of segments and the coordinates of the vertices of triangles, parallelograms, and trapezoids to solve problems in authentic contexts.
1. Classify triangles 2. Classify quadrilaterals I 3. Classify quadrilaterals II 4. Classify shapes on the coordinate plane: justify your answer

HS.GM.A.4 Use definitions of transformations and symmetry relationships to justify the solutions of problems in authentic contexts.		Transformations 1. Rotate polygons about a point 2. Transformations that carry a polygon onto itself Symmetry 3. Line symmetry 4. Rotational symmetry 5. Draw lines of symmetry 6. Count lines of symmetry
HS.GM.A.4 Use definitions of transformations and symmetry relationships to justify the solutions of problems in authentic contexts.
Transformations 1. Rotate polygons about a point 2. Transformations that carry a polygon onto itself Symmetry 3. Line symmetry 4. Rotational symmetry 5. Draw lines of symmetry 6. Count lines of symmetry

Checkpoint opportunity		1. Checkpoint: Congruence transformations 2. Checkpoint: Transformations in the plane
Checkpoint opportunity
1. Checkpoint: Congruence transformations 2. Checkpoint: Transformations in the plane
HS.GM.B Construct and communicate geometric arguments through use of proofs, logical reasoning, and geometric technology.
HS.GM.B.5 Apply and justify triangle congruence and similarity theorems in authentic contexts.		Congruent figures 1. Congruence statements and corresponding parts 2. Solve problems involving corresponding parts 3. Identify congruent figures Congruent triangles 4. SSS and SAS Theorems 5. ASA and AAS Theorems 6. SSS, SAS, ASA, and AAS Theorems 7. SSS Theorem in the coordinate plane Proofs involving congruent triangles 8. Proving triangles congruent by SSS and SAS 9. Proving triangles congruent by ASA and AAS 10. Proving triangles congruent by SSS, SAS, ASA, and AAS 11. Proofs involving corresponding parts of congruent triangles 12. Proofs involving triangles and quadrilaterals Isosceles and right triangles 13. Proofs involving isosceles triangles 14. Hypotenuse-Leg Theorem Similar figures 15. Ratios in similar figures 16. Similarity statements 17. Identify similar figures 18. Side lengths and angle measures in similar figures Similar triangles 19. Similar triangles and indirect measurement 20. Similarity rules for triangles 21. Triangle Proportionality Theorem 22. Similarity and altitudes in right triangles Proofs involving similar triangles 23. Prove similarity statements 24. Prove proportions or angle congruences using similarity 25. Prove the Pythagorean theorem
HS.GM.B.5 Apply and justify triangle congruence and similarity theorems in authentic contexts.
Congruent figures 1. Congruence statements and corresponding parts 2. Solve problems involving corresponding parts 3. Identify congruent figures Congruent triangles 4. SSS and SAS Theorems 5. ASA and AAS Theorems 6. SSS, SAS, ASA, and AAS Theorems 7. SSS Theorem in the coordinate plane Proofs involving congruent triangles 8. Proving triangles congruent by SSS and SAS 9. Proving triangles congruent by ASA and AAS 10. Proving triangles congruent by SSS, SAS, ASA, and AAS 11. Proofs involving corresponding parts of congruent triangles 12. Proofs involving triangles and quadrilaterals Isosceles and right triangles 13. Proofs involving isosceles triangles 14. Hypotenuse-Leg Theorem Similar figures 15. Ratios in similar figures 16. Similarity statements 17. Identify similar figures 18. Side lengths and angle measures in similar figures Similar triangles 19. Similar triangles and indirect measurement 20. Similarity rules for triangles 21. Triangle Proportionality Theorem 22. Similarity and altitudes in right triangles Proofs involving similar triangles 23. Prove similarity statements 24. Prove proportions or angle congruences using similarity 25. Prove the Pythagorean theorem

HS.GM.B.6 Justify theorems of line relationships, angles, triangles, and parallelograms; and use them to solve problems in authentic contexts.		Angles 1. Angle diagrams: solve for the variable 2. Angle bisectors 3. Proofs involving angles Parallel lines 4. Transversals of parallel lines: find angle measures 5. Proofs involving parallel lines I 6. Proofs involving parallel lines II Perpendicular bisectors 7. Perpendicular Bisector Theorem Triangles 8. Triangle Angle-Sum Theorem 9. Exterior Angle Theorem 10. Exterior Angle Inequality 11. Congruency in isosceles and equilateral triangles 12. Proofs involving isosceles triangles 13. Proofs involving triangles I 14. Proofs involving triangles II Parallelograms 15. Properties of parallelograms 16. Proving a quadrilateral is a parallelogram 17. Properties of rhombuses 18. Properties of squares and rectangles
HS.GM.B.6 Justify theorems of line relationships, angles, triangles, and parallelograms; and use them to solve problems in authentic contexts.
Angles 1. Angle diagrams: solve for the variable 2. Angle bisectors 3. Proofs involving angles Parallel lines 4. Transversals of parallel lines: find angle measures 5. Proofs involving parallel lines I 6. Proofs involving parallel lines II Perpendicular bisectors 7. Perpendicular Bisector Theorem Triangles 8. Triangle Angle-Sum Theorem 9. Exterior Angle Theorem 10. Exterior Angle Inequality 11. Congruency in isosceles and equilateral triangles 12. Proofs involving isosceles triangles 13. Proofs involving triangles I 14. Proofs involving triangles II Parallelograms 15. Properties of parallelograms 16. Proving a quadrilateral is a parallelogram 17. Properties of rhombuses 18. Properties of squares and rectangles

HS.GM.B.7 Perform 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
HS.GM.B.7 Perform 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

Checkpoint opportunity		1. Checkpoint: Line and angle theorems 2. Checkpoint: Parallelogram theorems 3. Checkpoint: Congruence and rigid motion 4. Checkpoint: Triangle similarity and congruence 5. Checkpoint: Dilations and similarity 6. Checkpoint: Triangle theorems 7. Checkpoint: Geometric constructions
Checkpoint opportunity
1. Checkpoint: Line and angle theorems 2. Checkpoint: Parallelogram theorems 3. Checkpoint: Congruence and rigid motion 4. Checkpoint: Triangle similarity and congruence 5. Checkpoint: Dilations and similarity 6. Checkpoint: Triangle theorems 7. Checkpoint: Geometric constructions
HS.GM.C Solve problems and interpret solutions of area and volume of shapes by applying concepts of congruence, similarity, symmetry in authentic contexts.
HS.GM.C.8 Solve authentic modeling problems using area formulas for triangles, parallelograms, trapezoids, regular polygons, and circles.		Quadrilaterals and triangles 1. Area of rectangles and squares 2. Area of parallelograms and triangles 3. Area of trapezoids 4. Area of rhombuses 5. Area of quadrilaterals: word problems Circles 6. Circles: word problems 7. Area and circumference of circles Irregular figures 8. Area of compound figures 9. Area between two shapes
HS.GM.C.8 Solve authentic modeling problems using area formulas for triangles, parallelograms, trapezoids, regular polygons, and circles.
Quadrilaterals and triangles 1. Area of rectangles and squares 2. Area of parallelograms and triangles 3. Area of trapezoids 4. Area of rhombuses 5. Area of quadrilaterals: word problems Circles 6. Circles: word problems 7. Area and circumference of circles Irregular figures 8. Area of compound figures 9. Area between two shapes

HS.GM.C.9 Use volume and surface area formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems and apply to authentic contexts.		Prisms and cylinders 1. Surface area and volume of rectangular prisms 2. Surface area of prisms and cylinders 3. Volume of prisms and cylinders Pyramids and cones 4. Surface area of pyramids and cones 5. Volume of pyramids and cones Spheres 6. Surface area of spheres 7. Volume of spheres Compound figures 8. Volume of compound figures
HS.GM.C.9 Use volume and surface area formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems and apply to authentic contexts.
Prisms and cylinders 1. Surface area and volume of rectangular prisms 2. Surface area of prisms and cylinders 3. Volume of prisms and cylinders Pyramids and cones 4. Surface area of pyramids and cones 5. Volume of pyramids and cones Spheres 6. Surface area of spheres 7. Volume of spheres Compound figures 8. Volume of compound figures

HS.GM.C.10 Use geometric shapes, their measures, and their properties to describe real world objects, and solve related authentic modeling and design problems.
HS.GM.C.10 Use geometric shapes, their measures, and their properties to describe real world objects, and solve related authentic modeling and design problems.


HS.GM.C.11 Apply concepts of density based on area and volume in authentic modeling situations.		Similar figures 1. Areas of similar figures 2. Perimeter and area: changes in scale Similar solids 3. Similar solids: find the missing length 4. Surface area and volume of similar solids 5. Surface area and volume: changes in scale 6. Perimeter, area, and volume: changes in scale Density 7. Calculate density, mass, and volume Geometric probability 8. Geometric probability
HS.GM.C.11 Apply concepts of density based on area and volume in authentic modeling situations.
Similar figures 1. Areas of similar figures 2. Perimeter and area: changes in scale Similar solids 3. Similar solids: find the missing length 4. Surface area and volume of similar solids 5. Surface area and volume: changes in scale 6. Perimeter, area, and volume: changes in scale Density 7. Calculate density, mass, and volume Geometric probability 8. Geometric probability

Checkpoint opportunity		1. Checkpoint: Surface area 2. Checkpoint: Volume 3. Checkpoint: Geometric modeling and design 4. Checkpoint: Density
Checkpoint opportunity
1. Checkpoint: Surface area 2. Checkpoint: Volume 3. Checkpoint: Geometric modeling and design 4. Checkpoint: Density
HS.GM.D Apply concepts of right triangle trigonometry in authentic contexts to solve problems and interpret solutions.
HS.GM.D.12 Apply sine, cosine, and tangent ratios, and the Pythagorean Theorem, to solve problems in authentic contexts.		Pythagorean theorem 1. Pythagorean theorem 2. Converse of the Pythagorean theorem 3. Pythagorean Inequality Theorems Trigonometric ratios 4. Trigonometric ratios: sin, cos, and tan 5. Trigonometric ratios with radicals: sin, cos, and tan 6. Trigonometric ratios in similar right triangles 7. Find trigonometric functions using a calculator 8. Inverses of trigonometric functions Special right triangles 9. Special right triangles 10. Find trigonometric functions of special angles 11. Solve a special right triangle Complementary angles 12. Sine and cosine of complementary angles Side lengths and angle measures 13. Trigonometric ratios: find a side length 14. Trigonometric ratios: find an angle measure 15. Solve a right triangle
HS.GM.D.12 Apply sine, cosine, and tangent ratios, and the Pythagorean Theorem, to solve problems in authentic contexts.
Pythagorean theorem 1. Pythagorean theorem 2. Converse of the Pythagorean theorem 3. Pythagorean Inequality Theorems Trigonometric ratios 4. Trigonometric ratios: sin, cos, and tan 5. Trigonometric ratios with radicals: sin, cos, and tan 6. Trigonometric ratios in similar right triangles 7. Find trigonometric functions using a calculator 8. Inverses of trigonometric functions Special right triangles 9. Special right triangles 10. Find trigonometric functions of special angles 11. Solve a special right triangle Complementary angles 12. Sine and cosine of complementary angles Side lengths and angle measures 13. Trigonometric ratios: find a side length 14. Trigonometric ratios: find an angle measure 15. Solve a right triangle

HS.GM.D.13 Apply the Pythagorean Theorem in authentic contexts, and develop the standard form for the equation of a circle.		Properties of circles 1. Find the center of a circle 2. Find the radius or diameter of a circle 3. Determine if a point lies on a circle Write equations 4. Derive equations of circles using the Pythagorean theorem 5. Write equations of circles in standard form from graphs 6. Write equations of circles in standard form using properties Graph circles 7. Graph circles from equations in standard form
HS.GM.D.13 Apply the Pythagorean Theorem in authentic contexts, and develop the standard form for the equation of a circle.
Properties of circles 1. Find the center of a circle 2. Find the radius or diameter of a circle 3. Determine if a point lies on a circle Write equations 4. Derive equations of circles using the Pythagorean theorem 5. Write equations of circles in standard form from graphs 6. Write equations of circles in standard form using properties Graph circles 7. Graph circles from equations in standard form

HS.GM.D.14 Use the coordinate plane to determine parallel and perpendicular relationships, and the distance between points.		Midpoints 1. Midpoint formula: find the midpoint 2. Partition a line segment in a given ratio 3. Midpoint formula: find the endpoint Distance 4. Distance formula Lines in the coordinate plane 5. Slopes of parallel and perpendicular lines 6. Equations of parallel and perpendicular lines 7. Find the distance between a point and a line 8. Find the distance between two parallel lines Classify shapes 9. Classify triangles 10. Classify quadrilaterals I 11. Classify quadrilaterals II 12. Classify shapes on the coordinate plane: justify your answer Area and perimeter 13. Area and perimeter in the coordinate plane I 14. Area and perimeter in the coordinate plane II
HS.GM.D.14 Use the coordinate plane to determine parallel and perpendicular relationships, and the distance between points.
Midpoints 1. Midpoint formula: find the midpoint 2. Partition a line segment in a given ratio 3. Midpoint formula: find the endpoint Distance 4. Distance formula Lines in the coordinate plane 5. Slopes of parallel and perpendicular lines 6. Equations of parallel and perpendicular lines 7. Find the distance between a point and a line 8. Find the distance between two parallel lines Classify shapes 9. Classify triangles 10. Classify quadrilaterals I 11. Classify quadrilaterals II 12. Classify shapes on the coordinate plane: justify your answer Area and perimeter 13. Area and perimeter in the coordinate plane I 14. Area and perimeter in the coordinate plane II

Checkpoint opportunity		1. Checkpoint: Right triangle trigonometry 2. Checkpoint: Equations of circles 3. Checkpoint: Coordinate proofs 4. Checkpoint: Distance and midpoints in the coordinate plane
Checkpoint opportunity
1. Checkpoint: Right triangle trigonometry 2. Checkpoint: Equations of circles 3. Checkpoint: Coordinate proofs 4. Checkpoint: Distance and midpoints in the coordinate plane