Module 2 builds on students' previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Reference Sheet for students with definitions and formulas used when looking at circles from a geometric perspective.

This concept review is a study guide for the Circles from a Geometric Perspective Unit, which is Module 7 from the Secondary Mathematics II Curriculum of Mathematics Vision Project.  Each concept that is covered in the review document has an accompanying video tutorial and set of guided notes that follow along with the videos.  Resources Included:1) Link to the Mathematics Vision Project Curriculum Module 7- Circles from a Geometric Perspective 2) Link to a Google Document containing links to videos and Guided Notes documents for each of the key concepts. Image, “Apollonian Gasket Variation” was created by fdecomite. This work is licensed under a Creative Commons Attribution 2.0 Generic License.

In this video segment you’ll discover how using concentric circles can help you determine how much paint is needed to cover the deck of a carousel.

Using circumference, this segment measures the total distant traveled by two carousel riders after the carousel has rotated 10 times.

The purpose of this task is to strengthen students' understanding of area. It could be assigned in class to individuals or small groups or given as a homework exercise to generate interesting discussions the following day. The relatively high levels of complexity and technical demand enhance its instructional value.

This lesson unit is intended to help teachers assess how well students are able to: use the Pythagorean theorem to derive the equation of a circle; and translate between the geometric features of circles and their equations.

This lesson unit is intended to help teachers assess how well students are able to: translate between the equations of circles and their geometric features; and sketch a circle from its equation.

This resource is an ordered outline for teachers who need guidance on what to cover for the geometry portion of the GED math test. Downloadable links are embedded in the outline as well as emphasis suggestions. The outline lists concepts to cover in a logical order for success on the geometry portion of the GED.

This site teaches the Geometry of Circles to High Schoolers through a series of 1084 questions and interactive activities aligned to 9 Common Core mathematics skills.

This geometry lesson shows that that an inscribed angle is half of a central angle that subtends the same arc. [Geometry playlist: Lesson 24 of 31]

This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties: solving problems by determining the lengths of the sides in right triangles; and finding the measurements of shapes by decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

CK-12's Texas Instruments Geometry Student Edition Flexbook is a useful collection of exercises intended to enrich a student's understanding of basic geometric principles.

Student-facing 7th grade math resources. Covers scale drawings, proportion, percentages, probability, expressions, and geometry.

In Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles.  The module begins with the definition of dilation, properties of dilations, and compositions of dilations.  One overarching goal of this module is to replace the common idea of “same shape, different sizes” with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

In this classic hands-on activity, learners estimate the length of a molecule by floating a fatty acid (oleic acid) on water. This lab asks learners to record measurements and make calculations related to volume, diameter, area, and height. Learners also convert meters into nanometers. Includes teacher and student worksheets but lacks in depth procedure information. The author suggests educators search the web for more complete lab instructions.

This task shows how to inscribe a circle in a triangle using angle bisectors. A companion task, ``Inscribing a circle in a triangle II'' stresses the auxiliary remarkable fact that comes out of this task, namely that the three angle bisectors of triangle ABC all meet in the point O.

This task is primarily for instructive purposes but can be used for assessment as well. Parts (a) and (b) are good applications of geometric constructions using a compass and could be used for assessment purposes but the process is a bit long since there are six triangles which need to be constructed.

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter.