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Common Core: Math
Subject: Math
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 Topic B begins with the definition of similarity and the properties of similarities. In Lesson 8, students learn that similarities map lines to lines, change the length of segments by factor r, and...

 Topic A begins by demonstrating the need for a precise definition of dilation instead of “same shape, different size” because dilation will be applied to geometric shapes that are not polygons. ...

 In Topic C, on the definition and properties of congruence, students learn that congruence is just a sequence of basic rigid motions. The fundamental properties shared by all the basic rigid motions...

 Topic B is a critical foundation to the understanding of congruence. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while...

 Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these...

 Student Outcomes Students use properties of similar triangles to solve realworld problems.

 Student Outcomes Students present informal arguments as to whether or not two triangles are similar. Students practice finding lengths of corresponding sides of similar triangles.

 Student Outcomes Students know an informal proof of the AngleAngle (AA) criterion for similar triangles. Students present informal arguments as to whether or not triangles are similar based on Angle...

 Student Outcomes Students know that similarity is both a symmetric and a transitive relation.

 Student Outcomes Students know the definition of similar and why dilation alone is not enough to determine similarity. Given two similar figures, students describe the sequence of a dilation and a...

 Student Outcomes Students know an informal proof of why dilations are degreepreserving transformations. Students know an informal proof of why dilations map segments to segments, lines to lines, and...

 Student Outcomes Students describe the effect of dilations on twodimensional figures using coordinates.

 Student Outcomes Students verify the converse of the Fundamental Theorem of Similarity experimentally. Students apply the Fundamental Theorem of Similarity to find the location of dilated points on...

 Student Outcomes Students experimentally verify the properties related to the Fundamental Theorem of Similarity (FTS).

 Student Outcomes Students know that dilations map circles to circles and ellipses to ellipses with the same shape. Students know that to shrink or magnify a dilated figure back to its original size...

 Student Outcomes § Students learn how to use a compass and a ruler to perform dilations. § Students learn that dilations map lines to lines, segments to segments, and rays to rays. Students know...

 Student Outcomes Students learn the definition of dilation and why “same shape” is not good enough to say two figures are similar. Students know that dilations magnify and shrink figures.

 Student Outcomes Students know a third informal proof of the angle sum theorem. Students know how to find missing interior and exterior angle measures of triangles and present informal arguments to...

 Student Outcomes Students know the Angle Sum Theorem for triangles; the sum of the interior angles of a triangle is always 180 degrees. Students present informal arguments to draw conclusions about...

 Student Outcomes Students know that corresponding angles, alternate interior angles, and alternate exterior angles of parallel lines are equal. Students know that when these pairs of angles are...

 Student Outcomes Students know the definition of congruence and related notation. Students know that to prove two figures are congruent there must be a sequence of rigid motions that maps one figure...

 Student Outcomes Students describe a sequence of rigid motions to map one figure onto another.

 Student Outcomes Students learn that the reflection is its own inverse transformation. Students understand that a sequence of a reflection followed by a translation is not equal to a translation...

 Student Outcomes Students learn that the reflection is its own inverse transformation. Students understand that a sequence of a reflection followed by a translation is not equal to a translation...