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Common Core: Standard
Common Core: ELA
Common Core: Math
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 Student Outcomes Students define a similarity transformation as the composition of basic rigid motions and dilations. Students define two figures to be similar if there is a similarity transformation...

 Student Outcomes Students know the properties of a similarity transformation are determined by the transformations that compose the similarity transformation. Students are able to apply a similarity...

 Student Outcomes Students understand that similarity is reflexive, symmetric, and transitive. Students recognize that if two triangles are similar, there is a correspondence such that corresponding...

 Student Outcomes Students prove the angleangle criterion for two triangles to be similar and use it to solve triangle problems.

 In the last lesson, students learned about the triangle side splitter theorem, which is now used to prove the dilation theorem. In Grade 8 students learned about the fundamental theorem of...

 In Grade 8, students informally showed that a dilation maps a segment to a segment on the coordinate plane. The lesson includes an opening discussion that reminds students of this fact. Next,...

 Student Outcomes Students prove that dilations map an angle to an angle with equal measure. Students understand how dilations map triangles, squares, rectangles, trapezoids, and regular polygons.

 Student Outcomes Students divide a line segment into equal pieces by the Side Splitter and Dilation Methods. Students know how to locate fractions on the number line.

 In Lesson 11, students examine the effects of dilating figures from two different centers. By experimental verification, they examine the impact on the two dilations of having two different scale...

 Student Outcomes Students create scale drawings of polygonal figures by the Parallel Method. Students explain why angles are preserved in scale drawings created by the Parallel Method using the...

 Student Outcomes Students understand that the Ratio and Parallel Methods produce the same scale drawing and understand the proof of this fact. Students relate the equivalence of the Ratio and...

 Students study and prove the properties of dilations.

 Student Outcomes Students review the properties of basic rigid motions. Students understand the properties of dilations and that a dilations is also an example of a transformation of the plane.

 Student Outcomes Students prove that a dilation maps a ray to a ray, a line to a line and a circle to a circle.

 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...

 Student Outcomes Students review properties of scale drawings and are able to create them.

 Student Outcomes Students create scale drawings of polygonal figures by the Ratio Method. Given a figure and a scale drawing from the Ratio Method, students answer questions about the scale factor...

 Student Outcomes: Students are able to derive a distance formula and apply it.

 Student Outcomes: Students find the perimeter of a triangle or quadrilateral in the coordinate plane given a description by inequalities. Students find the area of a triangle or quadrilateral in 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...

 Student Outcomes: Students find midpoints of segments and points that divide segments into 3, 4, or more proportional, equal parts.

 Student Outcomes: Using coordinates, students prove that the intersection of the medians of a triangle meet at a point that is twothirds of the way along each median from the intersected vertex....

 Student Outcomes: Students name several points on a line given by a parametric equation and provide the pointslope equation for a line given by a parametric equation. Students determine whether...

 Student Outcomes: Students state the relationship between previously used formats for equations for lines and the new format a1x + a2y + c, recognizing the segments from (0,0) to (a1, a2) as a normal...