Evidence of Understanding

**describe the center of dilation as the vertex of an angle**- experiment and describe relationships involving the
**center of dilation**by constructing line segments or figures along the two rays - explain why dilated lines not passing through the center of dilation are parallel and dilated lines passing through the center of dilation are superimposed

- experiment and describe relationships involving the
**identify and justify the center of dilation between dilated figures**- describe angle relationships using properties of parallel lines cut by a transversal

- describe angle relationships using properties of parallel lines cut by a transversal
**analyze relationships between corresponding sides and corresponding angles of dilated figures**- use tools to create and describe features of figures that are enlarged or reduced
- identify, using markings, corresponding angles that are congruent (
**ratio**is always 1:1) - explain the
**proportional**relationship between corresponding sides of a pre-image and its image - analyze the impacts of a dilation between dilated figures
- determine the
**scale factor**between a given preimage and image - apply the scale factor to determine measurements of a pre-image or its image
- explain why
**perimeter**maintains the scale factor and**area**squares the scale factor

- determine the

**determine the minimum criteria that proves polygons are similar (focusing on triangles)**- transform figures to distinguish and define
**congruence**and**similarity**- use the
*equality*of all corresponding pairs of angles (same shape) and the*proportionality*of all corresponding pairs of sides (scale factor) to define similarity - use coordinate notation with the plane to describe transformations

- use the
- identify the triangles, quadrilaterals, and other polygons that are always similar, sometimes similar or never similar and explain reasoning
- use tools and counterexamples to justify
**Angle-Angle (AA)**is valid criteria for triangle similarity- use the triangle angle sum theorem to describe why AA is sufficient minimum criteria

- compare the
**Side-Angle-Side (SAS)**and**Side-Side-Side (SSS)**criteria for congruence proofs versus similarity proofs- use tools and counterexamples to justify that two proportional sides and the congruent included angle is sufficient criteria for proving two triangles are similar

- justify why criteria for triangle congruence are also sufficient for proving triangle similarity
- explain congruence as a special case of similarity where the scale factor is 1

- transform figures to distinguish and define

Develop conceptual understanding:

dilation, center of dilation, ratio, proportional, scale factor, perimeter, area, similarity, AA, SAS, SSS, congruenceSupporting terms to communicate:

vertex, angle, segment, ray, corresponding, enlarge, reduce, parallel, transversal, preimage, image, transformation, rotation, reflection, translation