Essential Question:  How is similarity related to dilation and how does dilation affect area and volume?

Unit Rationale:  Extending the work of transformations and congruence to include shapes that are similar, connects what we know about area, volume, and proportionality.

As a result of this unit, students will be able to:

Ø  Identify, prove, and apply the properties of similar polygons.

Ø  Identify, prove, and apply the properties of similar triangles.

Ø  Use the properties of similarity to determine the measure of corresponding parts and their impact on the area and/or volume of shapes in 2 and 3 dimensions.

Vocabulary:

·        Dilation

·        Similar

·        Proportional

·        Indirect measurements

·        AA Similarity

·        SSS Similarity

·        SAS Similarity

Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements. 

Focus Standards:

*G.3.G  Know, prove, apply theorems about properties of quadrilaterals and other polygons.

*G.3.A  Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle.

*G.3.B  Determine and prove triangle congruence, triangle similarity, and other properties of triangles.

G.6.D  Predict and verify the effect that changing one, two, or three linear dimension has on perimeter, area, volume, or surface area of 2 and 3 dimensional figures.

Reasoning, Problem Solving, and Communication Standards:

G.7.D  Generalize a solution strategy for a single problem to a class of related problems and apply a strategy for a class of related problems to solve specific problems.

G.7.H  Use inductive reasoning to make conjectures , and use deductive reasoning to prove or disprove conjectures.

*G.7.G  Synthesize information to draw conclusions and evaluate the arguments and conclusions of others.