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Common Core: Standard
Common Core: ELA
Common Core: Math
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 Topic D brings in coordinate geometry to establish the equation of a circle. Students solve problems to find the equations of specific tangent lines or the coordinates of specific points of contact...

 The module concludes with Topic E focusing on the properties of quadrilaterals inscribed in circles and establishing Ptolemy's theorem. This result codifies the Pythagorean theorem, curious facts...

 In Topic C, students explore geometric relations in diagrams of two secant lines, or a secant and tangent line (possibly even two tangent lines), meeting a point inside or outside of a circle. They...

 Topic B defines the measure of an arc and establishes results relating chord lengths and the measures of the arcs they subtend. Students build on their knowledge of circles from Module 2 and prove...

 Topic A leads students first to Thales' theorem (an angle drawn from a diameter of a circle to a point on the circle is sure to be a right angle), then to possible converses of Thales' theorem, and...

 Students study the basic properties of twodimensional and threedimensional space, noting how ideas shift between the dimensions. They learn that general cylinders are the parent category for...

 Students begin their work with 3dimensions by first developing a stronger sense of area in two dimensions. They find approximated areas of curved figures by “squeezing” them between inscribed and...

 Students link their understanding of similarity and relationships within similar right triangles formally to trigonometry. In addition to the terms sine, cosine, and tangent, students study the...

 The focus in Topic D is similarity within right triangles. Students examine how an altitude drawn from the vertex of a right triangle to the hypotenuse creates two similar subtriangles. Students...

 Students learn what it means for two figures to be similar in general, and then focus on triangles and what criteria predict that two triangles will be similar. Length relationships within and...

 Students study and prove the properties of dilations.

 Students revisit what scale drawings are and discover two systematic methods of how to create them using dilations. The comparison of the two methods yield the Triangle Side Splitter Theorem and the...

 Students find midpoints of segments and points that divide segments into 3 or more equal and proportional parts and extend this concept prove classical results in geometry. Students are introduced...

 Students sketch the regions, determine points of intersection (vertices), and use the distance formula to calculate perimeter and the “shoelace” formula to determine area of these regions. Students...

 Students impose a coordinate system and describe the movement of the robot in terms of line segments and points. This leads to graphing inequalities and discovering regions in the plane can be...

 The challenge of programming robot motion along segments parallel or perpendicular to a given segment leads to an analysis of slopes of parallel and perpendicular lines. Students write equations for...

 Students begin this module with Topic A, Constructions. Major constructions include an equilateral triangle, an angle bisector, and a perpendicular bisector. Students synthesize their knowledge of...

 Constructions segue into Topic B, Unknown Angles, which consists of unknown angle problems and proofs. These exercises consolidate students’ prior body of geometric facts and prime students’...

 Topic C, Transformations, builds on students’ intuitive understanding developed in Grade 8. With the help of manipulatives, students observed how reflections, translations, and rotations behave...

 In Topic D, Proving Properties of Geometric Figures, students use what they have learned in Topics A through C to prove properties—those that have been accepted as true and those that are new—of...

 The module closes with a return to constructions in Topic E (G.CO.13).

 Topic F is a review that highlights how geometric assumptions underpin the facts established thereafter.

 In Topic G, students review material covered throughout the module. Additionally, students discuss the structure of geometry as an axiomatic system.