District of ColumbiaDC High School Geometry Curriculum
Video lessons and practice for every Geometry topic. Aligned to what DC high schools teach. Get help with proofs, transformations, and more.
DC High School Geometry Curriculum | StudyPugHelp
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.9 | Prove theorems about lines and angles. |
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.4 | Prove theorems about triangles. |
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.SRT.C.8 | Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. |
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.4 | Use coordinates to prove simple geometric theorems algebraically. |
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.HSF.IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. |
CC.HSS.ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. |
DC High School Geometry: What Students Learn
Washington DC high school Geometry covers a wide range of topics that build spatial reasoning and mathematical proof skills. Students move from foundational concepts like points, lines, and angles all the way through coordinate geometry and three-dimensional figures. StudyPug supports DC students at every step with clear video lessons and targeted practice problems.
Transformations and Congruence
One of the first major areas in Geometry is transformations. Students learn how rotations, reflections, and translations move figures in the plane, and how rigid motions define congruence. DC students explore congruence criteria like ASA, SAS, and SSS for triangles, and practice proving theorems about lines, angles, triangles, and parallelograms.
- Defining rotations, reflections, and translations using circles and lines
- Drawing transformed figures on graph paper or with geometry software
- Using rigid motions to determine if two figures are congruent
- Proving triangle congruence with ASA, SAS, and SSS
Similarity and Trigonometry
Students then explore similarity transformations and how they extend the idea of congruence. The AA similarity criterion for triangles leads directly into trigonometry, where students define sine, cosine, and tangent ratios for acute angles in right triangles. Applied problems using the Pythagorean Theorem and trigonometric ratios are a key part of this section.
- Dilations and scale factors
- AA, SAS, and SSS similarity criteria
- Sine, cosine, and tangent for acute angles
- Solving right triangles in real-world contexts
Circles
The circles unit covers inscribed angles, radii, chords, and tangent lines. Students prove that all circles are similar and derive the formula for arc length and sector area using the concept of radian measure. They also derive the standard equation of a circle using the Pythagorean Theorem and complete the square to find centers and radii from general equations.
- Relationships among inscribed angles, radii, and chords
- Inscribed and circumscribed circles of a triangle
- Arc length and radian measure
- Equation of a circle: standard and general form
Coordinate Geometry and Conic Sections
Students use coordinates to prove geometric theorems algebraically. This includes proving slope criteria for parallel and perpendicular lines, finding midpoints and partition points on line segments, and computing perimeters and areas using the distance formula. Students also derive equations for parabolas, ellipses, and hyperbolas.
- Slope criteria for parallel and perpendicular lines
- Partitioning a directed line segment
- Distance formula for perimeter and area
- Equations of parabolas, ellipses, and hyperbolas
Measurement, Modeling, and Algebra Connections
The final units bring together geometric measurement and real-world modeling. Students use volume formulas for cylinders, pyramids, cones, and spheres, and identify cross-sections of three-dimensional figures. They also apply geometric concepts to solve design problems and connect algebra skills — including creating and solving equations — to geometric contexts.
- Volume of cylinders, pyramids, cones, and spheres
- Two-dimensional cross-sections of 3D objects
- Density based on area and volume
- Creating and solving equations from geometric relationships