AlaskaAlaska High School Geometry Curriculum
Video lessons and practice for every high school Geometry topic. Aligned to Alaska Mathematics Standards so students can keep up, catch up, or get ahead.
Alaska 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. |
Alaska High School Geometry: Topics and Standards
Alaska high school Geometry follows the Alaska Mathematics Standards, which guide what students learn from foundational definitions through advanced coordinate and solid geometry. StudyPug covers every topic in this course with video lessons and practice problems so students can move at their own pace.
Transformations and Congruence
Students begin by learning precise definitions of geometric figures — points, lines, angles, and circles — before exploring transformations. Rotations, reflections, and translations are defined in terms of angles and lines. Students then use rigid motions to establish congruence and prove triangle congruence criteria including ASA, SAS, and SSS.
- Describing transformations as functions on the plane
- Predicting the effect of rigid motions on figures
- Proving theorems about lines, triangles, and parallelograms
- Formal geometric constructions with compass and straightedge
Similarity and Trigonometry
Similarity transformations extend congruence concepts. Students use the AA, SAS, and SSS similarity criteria to solve problems and prove relationships. Right triangle trigonometry introduces sine, cosine, and tangent ratios, and the Pythagorean Theorem is applied to real-world problems.
- Defining similarity in terms of transformations
- Establishing the AA criterion for triangle similarity
- Understanding sine and cosine of complementary angles
- Using trigonometric ratios to solve applied right triangle problems
Circles
Students prove that all circles are similar and explore relationships among inscribed angles, radii, and chords. They construct inscribed and circumscribed circles, derive arc length and sector area formulas, and develop the equation of a circle using the Pythagorean Theorem.
- Inscribed angle theorems and chord relationships
- Tangent lines from an external point
- Radian measure and arc length
- Deriving and applying the standard equation of a circle
Coordinate and Analytic Geometry
Coordinate geometry connects algebra and geometry. Students prove slope criteria for parallel and perpendicular lines, partition directed line segments, and use the distance formula to compute perimeters and areas. Conic sections — parabolas, ellipses, and hyperbolas — are derived from geometric definitions.
- Proving geometric theorems algebraically with coordinates
- Finding partition points on directed segments
- Deriving equations of parabolas, ellipses, and hyperbolas
- Computing polygon perimeters and areas using coordinates
Measurement, Modeling, and Three-Dimensional Geometry
Students apply volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Cross-sections of 3-D objects are identified, and geometric modeling is used to solve design problems involving density and area.
- Volume formulas and real-world applications
- Two-dimensional cross-sections of three-dimensional solids
- Density concepts based on area and volume
- Applying geometry to design and modeling contexts
Algebraic Connections in Geometry
Geometry at this level integrates algebraic reasoning. Students create and rearrange equations, solve systems involving linear and quadratic equations, and interpret expressions in geometric contexts. Scatter plots and data analysis also appear as students connect quantitative reasoning to geometric modeling.