Unit 4: Similarity |
Geometric & Spatial Reasoning (GSR) G.GSR.5: Describe dilations in terms of center and scale factor and use these terms to describe properties of dilations; use the precise definition of a dilation to describe similarity and establish the criterion to prove triangles to be similar; use these terms, definitions, and criterion to prove similarity, model, and explain real-life phenomena. |
STANDARD & Expectations | LT & SC Lesson Activities & Resources (LA&R) |
G.GSR.5.1 Verify experimentally the properties of dilations. | LT:
SC: I can identify a dilation as a reduction or enlargement depending on the scale factor. I can draw a dilation given the center at the origin and scale factor. I can identify the center of dilation using intersecting lines through corresponding preimage and image points. I can find the ratio of sides of the image to the preimage as the scale factor of a dilation. I can use function notation to represent dilations in the coordinate plane. I can describe properties of dilations such as center, scale factor, angle measure, parallelism, and collinearity.
LA&R: |
G.GSR.5.2 Given two figures, use and apply the definition of similarity in terms of similarity transformations. | LT:
SC: I can explain the meaning of similarity. I can identify when figures are similar based on corresponding angles being congruent, and corresponding sides being proportional. I can solve a proportion. I can apply properties of similarity to solve problems with missing values involving corresponding parts.
LA&R: |
G.GSR.5.3 Use the properties of similarity transformations to establish criterion for two triangles to be similar. Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures. | LT:
SC: I can apply properties of similarity to solve problems with missing values involving corresponding parts. I know when two triangles are similar based on AA, SSS, and SAS similarity postulates and theorems. I can prove two triangles are similar using appropriate methods (logic statements, paragraph proofs, two-column proofs, or flowchart proofs).
LA&R: |
G.GSR.5.4 Construct formal proofs to justify and apply theorems about triangles. | LT:
SC: I can prove a line parallel to one side of a triangle divides the other two proportionally, and its converse. I can use the Midsegment and Angle Bisector Theorems to solve problems in similar geometric figures. I can prove the Pythagorean Theorem using triangle similarity.
LA&R: |
