Massachusetts High School Geometry Curriculum

Video lessons and practice for every Geometry topic. Aligned to Massachusetts Mathematics Curriculum Framework standards for high school students.

Massachusetts High School Geometry Curriculum | StudyPugHelp

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ID

Standard

StudyPug Topic

CC.HSG.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.

CC.HSG.CO.A.2

Represent transformations in the plane using, e.g., transparencies and geometry software; 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.

CC.HSG.CO.A.3

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

CC.HSG.CO.B.6

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.

CC.HSG.CO.B.7

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.

CC.HSG.CO.B.8

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

CC.HSG.CO.C.10

Prove theorems about triangles.

CC.HSG.CO.C.11

Prove theorems about parallelograms.

CC.HSG.CO.D.12

Make formal geometric constructions with a variety of tools and methods.

CC.HSG.CO.D.13

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

CC.HSG.SRT.A.1

Verify experimentally the properties of dilations given by a center and a scale factor.

CC.HSG.SRT.A.2

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they 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.

CC.HSG.SRT.B.5

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

CC.HSG.SRT.C.6

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.

CC.HSG.SRT.C.7

Explain and use the relationship between the sine and cosine of complementary angles.

CC.HSG.C.A.1

Prove that all circles are similar.

CC.HSG.C.A.2

Identify and describe relationships among inscribed angles, radii, and chords.

CC.HSG.C.A.3

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

CC.HSG.C.A.4

Construct a tangent line from a point outside a given circle to the circle.

CC.HSG.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.

CC.HSG.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.

CC.HSG.GPE.A.2

Derive the equation of a parabola given a focus and directrix.

CC.HSG.GPE.A.3

Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

CC.HSG.GPE.B.5

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

CC.HSG.GPE.B.6

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

CC.HSG.GPE.B.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

CC.HSG.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.

CC.HSG.GMD.A.3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

CC.HSG.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.

CC.HSG.MG.A.1

Use geometric shapes, their measures, and their properties to describe objects.

CC.HSG.MG.A.2

Apply concepts of density based on area and volume in modeling situations.

CC.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context.

CC.HSA.SSE.B.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

CC.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

CC.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

CC.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

CC.HSA.CED.A.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

CC.HSA.REI.C.7

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

CC.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Massachusetts High School Geometry Topics

Geometry is a core high school math course in Massachusetts that builds the foundation students need for advanced mathematics. StudyPug covers every topic in the Massachusetts Mathematics Curriculum Framework for Geometry, from precise definitions and transformations all the way through coordinate geometry and 3D modeling.

Transformations and Congruence

Students begin by learning the precise definitions of geometric figures — angles, circles, perpendicular lines, parallel lines, and line segments. From there, the course moves into transformations: rotations, reflections, and translations. Students learn to describe transformations as functions and use rigid motions to define congruence. Triangle congruence criteria — ASA, SAS, and SSS — are developed directly from these definitions.

  • Rotations, reflections, and translations on the coordinate plane
  • Congruence in terms of rigid motions
  • Triangle congruence: ASA, SAS, SSS
  • Proofs about lines, angles, triangles, and parallelograms

Similarity and Trigonometry

Similarity transformations extend congruence concepts. Students use dilations and the AA criterion to prove triangles similar, then apply similarity to right triangle trigonometry. The sine, cosine, and tangent ratios arise naturally from side ratios in similar right triangles.

  • Dilations and similarity transformations
  • AA criterion for triangle similarity
  • Trigonometric ratios: sine, cosine, tangent
  • Pythagorean Theorem in applied problems
  • Complementary angle relationships for sine and cosine

Circles

The circles unit proves that all circles are similar and explores relationships among inscribed angles, radii, and chords. Students construct inscribed and circumscribed circles, work with arc length and radian measure, and derive the equation of a circle using the Pythagorean Theorem.

  • Inscribed angles and chord relationships
  • Arc length and radian measure
  • Area of a sector
  • Equation of a circle: standard form and completing the square
  • Equations of parabolas, ellipses, and hyperbolas

Coordinate Geometry

Coordinate geometry connects algebra and geometry. Students prove theorems algebraically using slope criteria for parallel and perpendicular lines, partition directed line segments, and compute perimeters and areas using the distance formula.

  • Slope criteria for parallel and perpendicular lines
  • Partitioning a directed line segment
  • Perimeters and areas using coordinates
  • Algebraic proofs of geometric theorems

Measurement and Modeling

The final units cover volume formulas for cylinders, pyramids, cones, and spheres, as well as cross-sections of 3D objects. Students apply geometric methods to real-world design and modeling problems, including density calculations based on area and volume.

  • Volume of cylinders, pyramids, cones, and spheres
  • Cross-sections of 3D figures
  • Density applications in modeling
  • Design problems using geometric methods

Aligned to Massachusetts Mathematics Curriculum Framework

Every StudyPug Geometry lesson is aligned to the Massachusetts Mathematics Curriculum Framework. Whether your student is preparing for daily homework, an upcoming test, or the 10th grade MCAS Math assessment, StudyPug covers the exact standards Massachusetts schools teach.