Unit Overview:

This unit extends the concepts from Unit 2 (Parallel Lines/Transformations) by transformations to further the concept of congruence and proofs.  The beginning of this unit starts out with the basic concept of congruence, which leads into proving congruence of triangles.  Students will then use these triangles to prove the properties of quadrilaterals.  Using the congruencies of triangles and rectangles students can calculate the areas of quadrilaterals.  In the next unit, students will be able to plot these quadrilaterals, and other geometric shapes, in the coordinate plane and find the midpoints and distance of the sides of these shapes.


Enduring Understanding:  

• Experimenting with transformations of rigid motion will lead to congruence in figures.
  
  
• Using the definition of congruence in figures will explain the criteria for triangle congruence.
  
  
• Triangle congruence will lead to the properties of quadrilaterals.
  
  
• Area can be developed by building shapes from triangles and rectangles.
  
  

Essential Question:

• How can congruence be defined by isometric transformations?
  
  

• How can isometric transformations be used to explain triangle congruence? (ASA, SAS, and SSS)
  
  
• How can you use the congruence postulates to prove two triangles are congruent?
  
  

• How will the triangle congruencies prove the properties of quadrilaterals?
  
  

• How can isometric transformations be used with triangles to formulate the area of quadrilaterals?