A. Algebra review

  1. Ratios and proportions
  2. Scale drawings: word problems
  3. Number sequences
  4. Shape patterns
  5. Properties of exponents
  6. Simplify radical expressions
  7. Write variable expressions
  8. Solve linear equations
  9. Solve linear inequalities
  10. Solve systems of linear equations
  11. Solve a quadratic equation by factoring
  12. Solve a quadratic equation using the quadratic formula

B. Points, lines, line segments, and planes

  1. Lines, line segments, and rays
  2. Properties of planes, lines, and points
  3. Describe intersections in a plane
  4. Lengths of segments on number lines
  5. Additive property of length
  6. Midpoints
  7. Congruent line segments
  8. Construct a congruent segment
  9. Perpendicular Bisector Theorem
  10. Midpoint formula: find the midpoint
  11. Partition a line segment in a given ratio
  12. Midpoint formula: find the endpoint
  13. Distance formula
  14. Distance to the origin in three dimensions
  15. Construct the midpoint or perpendicular bisector of a segment
    Checkpoint skill Checkpoint: Partition a line segment

C. Angles

  1. Angle vocabulary
  2. Angle measures
  3. Identify complementary, supplementary, vertical, adjacent, and congruent angles
  4. Find measures of complementary, supplementary, vertical, and adjacent angles
  5. Angle diagrams: solve for the variable
  6. Angle bisectors
  7. Construct an angle bisector
  8. Construct a congruent angle
  9. Proofs involving angles

D. Parallel and perpendicular lines

  1. Identify parallel, intersecting, and skew lines and planes
  2. Construct a perpendicular line
  3. Transversals: name angle pairs
  4. Transversals of parallel lines: find angle measures
  5. Transversals of parallel lines: solve for x
  6. Construct parallel lines
  7. Proofs involving parallel lines I
  8. Proofs involving parallel lines II
    Checkpoint skill Checkpoint: Definitions of geometric objects
    Checkpoint skill Checkpoint: Line and angle theorems

E. Lines in the coordinate plane

  1. Coordinate plane review
  2. Slopes of lines
  3. Graph a linear equation
  4. Equations of lines
  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
    Checkpoint skill Checkpoint: Coordinate proofs
    Checkpoint skill Checkpoint: Parallel and perpendicular lines

F. Introduction to triangles

  1. Classify triangles
  2. Triangle Angle-Sum Theorem
  3. Exterior Angle Theorem
  4. Exterior Angle Inequality

G. Two-dimensional figures

  1. Polygon vocabulary
  2. Interior angles of polygons
  3. Exterior angles of polygons
  4. Review: interior and exterior angles of polygons
  5. Construct an equilateral triangle or regular hexagon
  6. Construct a square

H. Three-dimensional figures

  1. Parts of three-dimensional figures
  2. Three-dimensional figure vocabulary
  3. Nets and drawings of three-dimensional figures
  4. Cross sections of three-dimensional figures
  5. Solids of revolution
    Checkpoint skill Checkpoint: Cross sections and solids of revolution

I. Logic

  1. Identify hypotheses and conclusions
  2. Counterexamples
  3. Conditionals
  4. Negations
  5. Converses, inverses, and contrapositives
  6. Biconditionals
  7. Truth tables
  8. Truth values

J. Introduction to congruent figures

  1. Congruence statements and corresponding parts
  2. Solve problems involving corresponding parts
  3. Identify congruent figures

K. Congruent triangles

  1. SSS and SAS Theorems
  2. Proving triangles congruent by SSS and SAS
  3. ASA and AAS Theorems
  4. Proving triangles congruent by ASA and AAS
  5. SSS, SAS, ASA, and AAS Theorems
  6. SSS Theorem in the coordinate plane
  7. Proving triangles congruent by SSS, SAS, ASA, and AAS
  8. Proofs involving corresponding parts of congruent triangles
  9. Congruency in isosceles and equilateral triangles
  10. Proofs involving isosceles triangles
  11. Hypotenuse-Leg Theorem

L. Transformations

  1. Classify congruence transformations
  2. Translations: graph the image
  3. Translations: find the coordinates
  4. Translations: write the rule
  5. Reflections: graph the image
  6. Reflections: find the coordinates
  7. Rotate polygons about a point
  8. Rotations: graph the image
  9. Rotations: find the coordinates
    • New! Reflections and rotations: write the rule
  10. Glide reflections: graph the image
  11. Sequences of congruence transformations: graph the image
  12. Sequences of congruence transformations: find the rules
  13. Transformations that carry a polygon onto itself
  14. Congruence transformations: mixed review
  15. Dilations: graph the image
  16. Dilations: find the coordinates
  17. Dilations: find length, perimeter, and area
  18. Dilations: find the scale factor
  19. Dilations: find the scale factor and center of the dilation
  20. Dilations and parallel lines
    Checkpoint skill Checkpoint: Transformations in the plane
    Checkpoint skill Checkpoint: Transformations of geometric figures
    Checkpoint skill Checkpoint: Rigid motion and congruence
    Checkpoint skill Checkpoint: Dilations

M. Triangles

  1. Midsegments of triangles
  2. Triangles and bisectors
  3. Identify medians, altitudes, angle bisectors, and perpendicular bisectors
  4. Angle-side relationships in triangles
  5. Triangle Inequality Theorem
  6. Construct the circumcenter or incenter of a triangle
  7. Construct the centroid or orthocenter of a triangle
  8. Find the centroid of a triangle
  9. Proofs involving triangles I
  10. Proofs involving triangles II
    Checkpoint skill Checkpoint: Triangle theorems

N. Quadrilaterals

  1. Identify trapezoids
  2. Classify quadrilaterals I
  3. Classify quadrilaterals II
  4. Find missing angles in quadrilaterals
  5. Graph quadrilaterals
  6. Properties of parallelograms
  7. Proving a quadrilateral is a parallelogram
  8. Properties of rhombuses
  9. Properties of squares and rectangles
  10. Properties of trapezoids
  11. Properties of kites
  12. Review: properties of quadrilaterals
  13. Classify shapes on the coordinate plane: justify your answer
  14. Proofs involving triangles and quadrilaterals
  15. Proofs involving quadrilaterals
    Checkpoint skill Checkpoint: Parallelogram theorems

O. Symmetry

  1. Line symmetry
  2. Rotational symmetry
  3. Draw lines of symmetry
  4. Count lines of symmetry

P. Similarity

  1. Similarity ratios
  2. Similarity statements
  3. Identify similar figures
  4. Side lengths and angle measures in similar figures
  5. Similar triangles and indirect measurement
  6. Perimeters of similar figures
  7. Angle-angle criterion for similar triangles
  8. Similarity rules for triangles
  9. Similar triangles and similarity transformations
  10. Similarity of circles
  11. Triangle Proportionality Theorem
  12. Similarity and altitudes in right triangles
  13. Areas of similar figures
  14. Prove similarity statements
  15. Prove proportions or angle congruences using similarity
  16. Proofs involving similarity in right triangles
    Checkpoint skill Checkpoint: Similarity transformations
    Checkpoint skill Checkpoint: Triangle similarity and congruence
    Checkpoint skill Checkpoint: Prove circles are similar

Q. Pythagorean theorem

  1. Pythagorean theorem
  2. Prove the Pythagorean theorem
  3. Converse of the Pythagorean theorem
  4. Pythagorean Inequality Theorems

R. Trigonometry

  1. Trigonometric ratios: sin, cos, and tan
  2. Trigonometric ratios: csc, sec, and cot
  3. Trigonometric ratios in similar right triangles
  4. Special right triangles
  5. Find trigonometric functions of special angles
  6. Solve a special right triangle
  7. Find trigonometric functions using a calculator
  8. Sine and cosine of complementary angles
  9. Inverses of trigonometric functions
  10. Trigonometric ratios: find a side length
  11. Trigonometric ratios: find an angle measure
  12. Solve a right triangle
  13. Law of Sines
  14. Law of Cosines
  15. Solve a triangle
  16. Area of a triangle: sine formula
  17. Area of a triangle: Law of Sines
    Checkpoint skill Checkpoint: Right triangle trigonometry
    Checkpoint skill Checkpoint: Laws of Sines and Cosines

S. Area and perimeter

  1. Perimeter
  2. Area of rectangles and squares
  3. Area of parallelograms and triangles
  4. Area of trapezoids
  5. Area of rhombuses
    • New! Area of regular polygons
  6. Area and perimeter in the coordinate plane I
  7. Area and perimeter in the coordinate plane II
  8. Area and circumference of circles
  9. Area of compound figures
  10. Area between two shapes
  11. Area and perimeter of similar figures
  12. Perimeter and area: changes in scale
  13. Heron’s formula
  14. Area and perimeter mixed review
    Checkpoint skill Checkpoint: Area and perimeter in the coordinate plane

T. Surface area and volume

  1. Surface area and volume of rectangular prisms
  2. Surface area of prisms and cylinders
  3. Surface area of pyramids and cones
  4. Surface area of spheres
  5. Volume of prisms and cylinders
  6. Volume of pyramids and cones
  7. Volume of spheres
  8. Volume of compound figures
  9. Similar solids: find the missing length
  10. Surface area and volume of similar solids
  11. Surface area and volume: changes in scale
  12. Perimeter, area, and volume: changes in scale
  13. Surface area and volume review
    Checkpoint skill Checkpoint: Volume

U. Circles

  1. Parts of a circle
  2. Central angles and arc measures
  3. Understand arc length and sector area of a circle
  4. Arc length
  5. Convert between radians and degrees
  6. Radians and arc length
  7. Area of sectors
  8. Circle measurements: mixed review
  9. Arcs and chords
  10. Tangent lines
  11. Perimeter of polygons with an inscribed circle
  12. Inscribed angles
  13. Angles in inscribed right triangles
  14. Angles in inscribed quadrilaterals I
  15. Angles in inscribed quadrilaterals II
  16. Angles formed by chords, secants, and tangents
  17. Segments formed by chords, secants, and tangents
  18. Construct a tangent line to a circle
  19. Construct an equilateral triangle inscribed in a circle
  20. Construct a square inscribed in a circle
  21. Construct a regular hexagon inscribed in a circle
  22. Construct the inscribed or circumscribed circle of a triangle
    Checkpoint skill Checkpoint: Angles and lines in circles
    Checkpoint skill Checkpoint: Inscribed and circumscribed circles
    Checkpoint skill Checkpoint: Arc length and area of sectors
    Checkpoint skill Checkpoint: Geometric constructions

V. Circles and parabolas in the coordinate plane

  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
  4. Write equations of circles in standard form from graphs
  5. Write equations of circles in standard form using properties
  6. Convert equations of circles from general to standard form
  7. Find properties of circles from equations in general form
  8. Graph circles from equations in standard form
  9. Graph circles from equations in general form
  10. Find the vertex of a parabola
  11. Find the focus or directrix of a parabola
  12. Find the axis of symmetry of a parabola
  13. Write equations of parabolas in vertex form from graphs
  14. Write equations of parabolas in vertex form using the focus and directrix
  15. Write equations of parabolas in vertex form using properties
  16. Convert equations of parabolas from general to vertex form
  17. Find properties of a parabola from equations in general form
  18. Graph parabolas
    Checkpoint skill Checkpoint: Equations of circles
    Checkpoint skill Checkpoint: Equations of parabolas

W. Measurement

  1. Convert rates and measurements: customary units
  2. Convert rates and measurements: metric units
  3. Convert square and cubic units of length
  4. Precision
  5. Greatest possible error
  6. Minimum and maximum area and volume
  7. Percent error
  8. Percent error: area and volume
  9. Calculate density, mass, and volume
    Checkpoint skill Checkpoint: Geometric modeling and design
    Checkpoint skill Checkpoint: Density

X. Probability

  1. Theoretical and experimental probability
  2. Outcomes of compound events
  3. Identify independent and dependent events
  4. Probability of independent and dependent events
  5. Counting principle
  6. Permutations
  7. Permutation and combination notation
  8. Find probabilities using combinations and permutations
  9. Find probabilities using two-way frequency tables
  10. Identify independent events
  11. Find conditional probabilities
  12. Independence and conditional probability
  13. Find conditional probabilities using two-way frequency tables
  14. Geometric probability
  15. Find probabilities using the addition rule
    Checkpoint skill Checkpoint: Understand independence and conditional probability
    Checkpoint skill Checkpoint: Probabilities of compound events

Y. Vectors

  1. Compass directions and vectors
  2. Find the magnitude of a vector
  3. Find the component form of a vector
  4. Find the component form of a vector given its magnitude and direction angle
  5. Graph a resultant vector using the triangle method
  6. Graph a resultant vector using the parallelogram method
  7. Add vectors
  8. Subtract vectors