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Common Core: Standard
Common Core: ELA
Common Core: Math
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 Geometry Module 1: Congruence, Proof, and Constructions Module 1 embodies critical changes in Geometry as outlined by the Common Core. The heart of the module is the study of transformations and the...

 Student Outcomes Students learn to construct an equilateral triangle. Students communicate mathematic ideas effectively and efficiently.

 Student Outcomes Students apply the equilateral triangle construction to more challenging problems. Students communicate mathematical concepts clearly and concisely.

 Student Outcomes Students learn how to bisect an angle as well as how to copy an angle.

 Student Outcome Students learn to construct a perpendicular bisector and about the relationship between symmetry with respect to a line and a perpendicular bisector.

 Student Outcome Students become familiar with vocabulary regarding two points of concurrencies and understand why the points are concurrent.

 Student Outcomes Students review formerly learned geometry facts and practice citing the geometric justifications in anticipation of unknown angle proofs.

 Student Outcomes Students review formerly learned geometry facts and practice citing the geometric justifications in anticipation of unknown angle proofs.

 Student Outcome Students review formerly learned geometry facts and practice citing the geometric justifications regarding angles in a triangle in anticipation of unknown angle proofs.

 Student Outcome Students write unknown angle proofs, which does not require any new geometric facts. Rather, writing proofs requires students to string together facts they already know to reveal...

 Student Outcome Students write unknown angle proofs involving auxiliary lines.

 Student Outcomes Students write unknown angle proofs involving known facts.

 Student Outcomes Students discover the gaps in specificity regarding their understanding of transformations. Students identify the parameters they need to complete any rigid motion.

 Student Outcomes Students manipulate rotations by each parameter—center of rotation, angle of rotation, and a point under the rotation.

 Student Outcomes Students learn the precise definition of a reflection. Students construct the line of reflection of a figure and its reflected image. Students construct the image of a figure when...

 Student Outcomes Students learn the relationship between a reflection and a rotation. Students examine rotational symmetry within an individual figure.

 Student Outcome Students learn the precise definition of a translation and perform a translation by construction.

 Student Outcomes Students understand that any point on a line of reflection is equidistant from any pair of preimage and image points in a reflection.

 Student Outcomes Students learn to construct a line parallel to a given line through a point not on that line using a rotation by 180˚. They learn how to prove the alternate interior angles theorem...

 Student Outcomes Students begin developing the capacity to speak and write articulately using the concept of congruence. This involves being able to repeat the definition of congruence and use it in...

 Student Outcomes Students will understand that a congruence between ﬁgures gives rise to a correspondence between parts such that corresponding parts are congruent, and they will be able to state the...

 Student Outcomes Students practice applying a sequence of rigid motions from one figure onto another figure in order to demonstrate that the figures are congruent.

 Student Outcomes Students learn why any two triangles that satisfy the SAS congruence criterion must be congruent.

 Student Outcomes Students examine two different proof techniques via a familiar theorem. Students complete proofs involving properties of an isosceles triangle.