Geometry Course Details

Building unique learning experiences with the courses mapped to the national standards.

img

imgDiagnostic Test

Evaluate your kid’s strengths,
proficiency level and gaps for FREE!

Start Now

Course Metrics

  • Common Core Geometry SkillsSkills
    170
  • Coomon Core Geometry TutorialsTutorials
    338
  • Common Core Geometry Video LessonsVideo Lessons
    58
  • Free Response Questions for Online Geometry CourseExamples
    888
  • Online practice assessments for GeometryFree Response Questions
    6238
  • Geometry Off-line Practice SheetsMultiple Choice Questions
    1313
  • Math Activities for GeometryOnline Practice Assessments
    72
  • Graded Assesments for online geometry courseGraded Assessments
    74
Select This Course Take a Free Diagnostic Test

Overview

ELC offers powerful content for Math including features to engage students to learn, empower parents' involvement, and for teaching in a traditional classroom environment or virtual learning environment (Hybrid or online course).

All courses provide customized pre-requisite topics for review, 100% of standard topics for common core standards, and additional advanced topics to help students get ahead. Educo also provides the content to support each step of the learning process (tutorials, examples, practice, assessment, and detailed analytics for review)

"I Can" Statements For Math Geometry

Mathematics | High School—Geometry

Domain: Congruence

HSG-CO

Cluster: Experiment with transformations in the plane
Standard HSG-CO.A.1
Standard Description 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.
Online Corse Hierarchy 1.1
I Can Statements I can understand the basic terms used in geometry, like angles, line, line segments, point, parallel and perpendicular lines.
I can measure line segments.
Standard HSG-CO.A.2
Standard Description 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 (e.g., translation versus horizontal stretch).
Online Corse Hierarchy 1.2, 1.4, 1.5
I Can Statements I can define polar coordinates and convert polar to rectangular coordinates and vice-versa.
I can define transformations – reflections, rotations, translations, and dilations.
Standard HSG-CO.A.3
Standard Description 3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Online Corse Hierarchy 1.4, 1.5
I Can Statements I can define reflections and rotations in polygons.
Standard HSG-CO.A.4
Standard Description 4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Online Corse Hierarchy 1.6
I Can Statements I can define the composition of isometries.
Standard HSG-CO.A.5
Standard Description 5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another
Online Corse Hierarchy 1.3
I Can Statements I can define symmetry and rotational symmetry.
Standard HSG-CO.B.6
Standard Description 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.
Online Corse Hierarchy 4.1
I Can Statements I can use the definition of congruence in terms of rigid motions to decide if they are congruent.
Standard HSG-CO.B.7
Standard Description 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 angles are congruent.
Online Corse Hierarchy 4.1
I Can Statements I can 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 angles are congruent.
Standard HSG-CO.B.8
Standard Description 8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Online Corse Hierarchy 4.1, 4.2
I Can Statements I can define different criteria of triangle congruence (ASA, SAS, SSS, and RHS)
Standard HSG-CO.C.9
Standard Description 9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent, and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Online Corse Hierarchy 2.1, 2.2, 2.3
I Can Statements I can define types of angles and angle measurements.
I can define special angle pairs.
I can define parallel lines, transversal, and angle pairs.
I can prove theorems about lines and angles.
Standard HSG-CO.C.10
Standard Description 10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Online Corse Hierarchy 3.1, 3.2, 3.3
I Can Statements I can define triangles and their properties.
I can define centroid, orthocenter, circumcenter, and incenter and theorems about triangles.
I can define inequalities in a triangle.
Standard HSG-CO.C.11
Standard Description 11. Prove theorems about parallelograms.
Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
Online Corse Hierarchy 5.1, 5.2
I Can Statements I can define parallelograms and their basic properties.
I can prove theorems about parallelograms.
I can prove the Mid-Point theorem.
Standard HSG-CO.D.12
Standard Description 12. Make formal geometric constructions with various tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point, not on the line.
Online Corse Hierarchy 2.4
I Can Statements I can construct a line parallel to a given line, perpendicular lines, perpendicular bisector, angles and angle bisector.
Standard HSG-SRT.A.1
Standard Description 1. Verify experimentally the properties of dilations given by a center and a scale factor:
a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Online Corse Hierarchy 8.1
I Can Statements I can understand dilations and similarities.
Standard HSG-SRT.A.2
Standard Description 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.
Online Corse Hierarchy 8.1
I Can Statements I can understand the concept of similarity.
Standard HSG-SRT.A.3
Standard Description 3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Online Corse Hierarchy 8.4, 8.5
I Can Statements I can define conditions for the similarity of triangles.
I can find areas of similar triangles.
Standard HSG-SRT.B.4
Standard Description 4. Prove theorems about triangles.
Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely, the Pythagorean Theorem proved using triangle similarity.
Online Corse Hierarchy 8.2, 8.3
I Can Statements I can prove theorems about triangles (Basic Proportionality theorem)
and Pythagoras theorem).
Standard HSG-SRT.B.5
Standard Description 5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Online Corse Hierarchy 8.2
I Can Statements I can use similarity criteria for triangles to solve problems.
Standard HSG-SRT.C.6
Standard Description 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.
Online Corse Hierarchy 9.1, 9.2, 9.3, 9.4
I Can Statements I can define trigonometric functions and trigonometric identities.
Standard HSG-SRT.C.7
Standard Description 7. Explain and use the relationship between the sine and cosine of complementary angles.
Online Corse Hierarchy 9.2, 9.3, 9.4, 9.5
I Can Statements I can explain and use the relationship between the sine and cosine of complementary angles.
Standard HSG-SRT.C.8
Standard Description 8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Online Corse Hierarchy 9.6
I Can Statements I can use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Standard HSG-SRT.D.9
Standard Description 9. (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
Online Corse Hierarchy 9.7, 9.8
I Can Statements I can derive the formula
A = 1/2 ab sin(C) for the area of a triangle
Standard HSGSRT.D.10
Standard Description 10. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
Online Corse Hierarchy 9.7, 9.8
I Can Statements I can prove the Laws of Sines and Cosines and use them to solve problems.
Standard HSGSRT.D.11
Standard Description 11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Online Corse Hierarchy 9.7, 9.8
I Can Statements I can understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
I can graph sine and cosine functions.
Standard HSG-C.A.2
Standard Description 2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
Online Corse Hierarchy 10.1, 10.2
I Can Statements I can describe relationships among inscribed angles, radii, chords, and arcs.
Standard HSG-C.A.3
Standard Description 3. Construct the inscribed and circumscribed circles of a triangle and prove the properties of angles for a quadrilateral inscribed in a circle.
Online Corse Hierarchy 10.3
I Can Statements I can describe angles formed in the interior and exterior of a circle and theorems about them,
I can prove the properties of angles for a quadrilateral inscribed in a circle. (cyclic quadrilateral)
Standard HSG-C.A.4
Standard Description 4. (+) Construct a tangent line from a point outside a given circle to the circle.
Online Corse Hierarchy 10.4
I Can Statements I can construct a tangent line from a point outside a given circle to the circle and use theorems about them to solve problems.
Standard HSG-C.B.5
Standard Description 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.
Online Corse Hierarchy 10.5, 10.6, 10.7, 10.8
I Can Statements I can define the arcs and segments of a circle.
I can define the radian measure of the angle.
I can derive the formula for a sector's area and a circle's segment.
Standard HSG-GPE.A.1
Standard Description 1. Derive the equation of a circle of a given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Online Corse Hierarchy 11.1
I Can Statements I can derive the equation of a circle of a given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Standard HSG-GPE.A.2
Standard Description 2. Derive the equation of a parabola given a focus and directrix.
Online Corse Hierarchy 11.2
I Can Statements I can define parabolas and derive the parabola equation given a focus and directrix.
Standard HSG-GPE.A.3
Standard Description 3. (+) Derive the equations of ellipses and hyperbolas given foci and directrices.
Online Corse Hierarchy 11.3, 11.4
I Can Statements I can define ellipses and hyperbolas and derive the equations of ellipses and hyperbolas given foci and directrices.
Standard HSG-GPE.B.4
Standard Description 4. Use coordinates to prove simple geometric theorems algebraically.
For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
Online Corse Hierarchy 12.1
I Can Statements I can define coordinate plane, complete tables and graph equations using points and intercepts.
Standard HSG-GPE.B.5
Standard Description 5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Online Corse Hierarchy 12.1, 12.2, 12.3
I Can Statements I can define slope and slope criteria for parallel and perpendicular lines (and use them to solve geometric problems).
I can find equations of lines in different forms.
Standard HSG-GPE.B.6
Standard Description 6. Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Online Corse Hierarchy 12.5
I Can Statements I can partition a line segment using the section formula.
Standard HSG-GPE.B.7
Standard Description 7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Online Corse Hierarchy 12.4
I Can Statements I can use the distance and midpoint formulas to compute the perimeters of polygons and areas of triangles and rectangles.
Standard HSGGMD.A.1
Standard Description 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. Use dissection arguments, Cavalieri's principle, and informal limit arguments.
Online Corse Hierarchy 6.1, 6.2
I Can Statements I can find the perimeter and area of polygons.
I can find the circumference and area of a circle.
Standard HSGGMD.A.2
Standard Description 2. (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
Online Corse Hierarchy 7.2
I Can Statements I can define Cavalieri's principle.
I can find the surface area and volume of the sphere and prism.
Standard HSGGMD.A.3
Standard Description 3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Online Corse Hierarchy 7.1, 7.2, 7.3
I Can Statements I can find the surface area and volume of cylinders, cones, pyramids, and tetrahedrons.
Download Curriculum

Features

The ELC platform integrates well-known children's learning pedagogies with standardaligned courses for grades 1 to 12. It features an easy-to-use workflow for learning, practicing, and assessing student performance
Student features for Learning and Parent features for Monitoring and Support
Diagnostic Test and Analytics Open Green Lock
Measures students' understanding of math knowledge skills beforehand for the current grade. Free with registration
Prerequisites Topics (Chapter 0) Open Green Lock
Review recommended prerequisite topics based on diagnostic test results. Free with registration
Grade level Topics Closed Red Lock
Aligned to common core standards, includes all the standards topics With paid subscription
Advanced Topics Closed Red Lock
Additional topics for advanced skills With paid subscription
Digital Tutorials & Illustrations Closed Red Lock
Interactive step-by-step tutorials with discussions, illustrations, and examples. Also used by teachers in a digital or hybrid classroom. With paid subscription
Online Practice Sheets Closed Red Lock
Students get unlimited attempts for practice organized by topics, sections, or chapters. Students get immediate feedback through a solution for all the questions With paid subscription
Download Practice Sheets (Print) Closed Red Lock
Download and print a practice sheet for offline practice. You can print without answers, with answers, and with solutions. With paid subscription
Math Activities Closed Red Lock
Available for grades 1 to 5 courses With paid subscription
Graded Assessment Closed Red Lock
Quizzes and tests at a topic, section, and chapter levels to gauge performance With paid subscription
eWorkbook Closed Red Lock
Sold separately and in combination with an ELC subscription. An excellent resource for quick review and additional practice With paid subscription
Analytics and Reports Closed Red Lock
Reports & Analytics are available for students & parents
Diagnostic Report
Skills Report
Standards Report
Graded Assessment Score Reports
Time Spent Report		 With paid subscription
Student Dashboard Open Green Lock
Provides information on students' activities and performance. Free with registration
Parent Dashboard Open Green Lock
Provides information and support tools to help their child learn and monitor Free with registration
Parent View Open Green Lock
Parents can view the tutorials, practice, and assessments to monitor and support their students Free with registration
Teachers/Tutors Features to help Students Learn Online or in a Classroom
Prerequisites Topics (Chapter 0) Open Green Lock
Review recommended prerequisite topics based on diagnostic test results. Free with registration
Grade level Topics Open Green Lock
Aligned to common core standards, includes all the standards' topics Free with registration
Advanced Topics Open Green Lock
Additional topics for advanced skills Free with registration
Digital Tutorials & Illustrations Open Green Lock
Interactive step-by-step tutorials with discussions, illustrations, and examples. Also used by teachers in a digital or hybrid classroom. Free with registration
Download Practice Sheets (Print) Open Green Lock
Download and print a practice sheet for offline practice. You can print without answers, with answers, and with solutions. Free with registration

Introduction to the Common Core State Standards

Satisfied Mother and her Daughter sitting together are looking at a laptop

The Common Core State Standards are an excellent resource for parents and educators alike. They provide a clear outline of what skills and knowledge children should acquire at each grade level, making it easier to support their learning. By following these standards, students can also be better prepared for college, entry-level professions, and vocational training programs after graduation. It's reassuring to know there's a clear path to success for our children.

ELC courses cover 100% of skills defined in Common Core Math Standards for Geometry. In addition to CCSS skills, our Geometry course covers essential pre-requisites skills from previous grades for review and more advanced skills for students who want to get ahead.

The standards do not prescribe the specific curriculum or methods of teaching. Instead, they provide a framework of skills and knowledge that student should acquire in order to be successful. The curriculum and teaching method are decided by the teachers and our experienced teachers have designed the course hierarchy to ensure that children learn the skills in proper sequence.

It is difficult to decipher the standards and we have done the work to make sure that a parent or teacher can easily understand the standard. We provide easy-to-understand “I Can Do” checklists in infographics or table format. These checklists outline skills your child should know for each grade. You can download the “I Can Do” checklists to understand what skills your child should know for the grade from our course page.

How to read the Geometry level standards?

How to read the Grade Level Standards

Geometry Domains Summary:

Geometry Domains Summary with Category and Topics

The following table summarizes what Math domains are covered in K-12 grades:

What Math Domains are Covered in K-12 Grades

Click here to discover the comprehensive Common Core State Standards.

Download Curriculum