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Pennsylvania Geometry | StudyPug Online Math HelpHelp
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. |
Complete Geometry Coverage
Topics
108
Video Lessons
692
Practice Questions
617
Study Time
~140 hours
Why Pennsylvania Geometry Students Love StudyPug
Built specifically for Pennsylvania high school success
Pennsylvania Curriculum Aligned
Every lesson matches Pennsylvania Geometry standards—what you learn in class, we teach
Keystone Exam Prep
Practice with Pennsylvania Keystone Algebra I assessment questions—be ready for exam day
Certified PA Teachers
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Frequently Asked Questions
Everything you need to know about mastering Geometry with StudyPug
What does Geometry coverage include?
StudyPug covers all Pennsylvania Geometry standards: congruence and triangle proofs, transformations and similarity, circle theorems and angles, trigonometric ratios, coordinate geometry with lines and conic sections, 3D geometry including volume and surface area, and complete proof-writing. With 692 video lessons across 115 topics, you'll find every concept from your textbook—transformations, parallel lines, quadrilaterals, circles, similarity, right triangles, and coordinate proofs.
How does photo search work?
Snap a photo of any Geometry problem—whether it's triangle congruence, circle theorems, or coordinate geometry. StudyPug's AI identifies the concept and shows you the exact video lesson teaching that topic. Find the right help in seconds instead of searching through hundreds of videos. It works for proofs, constructions, calculations, and word problems. Upload from your phone during homework or studying—get instant access to step-by-step explanations that match your specific problem type.
How many practice problems are available?
You get unlimited practice with 677 Geometry questions covering every topic. Work through triangle congruence proofs, circle angle calculations, trigonometric ratios, coordinate geometry problems, and 3D volume questions. Every problem includes full step-by-step solutions so you understand exactly where you went wrong. Questions adapt to your level—if you're struggling, you'll get easier variations; when you're ready, harder problems challenge you. Practice until concepts truly stick, then track your mastery progress.
What if I'm falling behind in Geometry?
Start exactly where you need help—no judgment, just learning. Use photo search to find lessons for concepts you missed, then work through practice problems at your own pace. Video lessons let you pause, rewind, and rewatch until things click. The adaptive practice identifies your weak spots and gives you targeted questions to build confidence. Thousands of Pennsylvania students have caught up and improved their grades using StudyPug. Whether you're struggling with proofs, circle theorems, or trig, we break down every concept into manageable steps.
Does StudyPug help with Geometry exams?
Yes! StudyPug prepares you for chapter tests, semester exams, and the Pennsylvania Keystone assessments. Practice with questions that match real exam formats—multiple choice, constructed response, and proof writing. Focus on high-stakes topics like triangle congruence, circle theorems, coordinate geometry, and trigonometry. Review video lessons before tests to refresh concepts, then take practice quizzes that simulate exam conditions. Track which topics you've mastered and which need more work, so you study efficiently and walk into exams confident.
How much does StudyPug cost?
StudyPug offers flexible plans starting as low as a few dollars per month with annual subscriptions. You get unlimited access to all 692 Geometry video lessons, 677 practice questions, photo search, and progress tracking—no limits on how much you can learn. One subscription costs less than a single tutoring session but gives you 24/7 help all year. Try it risk-free to see if it works for you. Most students say it's the best investment they've made in their grades, saving them from expensive tutors while delivering better results.
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