Parallel Lines & Transversals Common Core Investigation 4: Geometry Topics

Learning Goal 3(8.G.A.5): The student will understand and use informal arguments to prove congruency and similarity using physical models, transparencies or geometry software. 4 3 2 1 In addition to level 3.0 and above and beyond what was taught in class, I may: Make connection with real-world situations Make connection with other concepts in math Make connection with other content areas.  I understand and use informal arguments to prove congruency and similarity using physical models, transparencies or geometry software. understand the relationship between the measure of an exterior angle and the other angles of a triangle find and prove the measure of a missing angle of a triangle explain the relationship of the angles formed when parallel lines are cut by a transversal use vocabulary associated with parallel lines cut by a transversal informally prove similarity of triangles I understand congruency and similarity using physical models, transparencies or geometry software. construct triangles find the measure of a missing angle in triangle find missing angles of parallel lines cut by a transversal   With help from the teacher, I have partial success with the unit content. Even with help, I have no success with the unit content.

Definitions: Parallel Lines: Two lines that never intersect. Transversal: A line that intersects two or more lines. When parallel lines are intersected by a transversal, many angles are formed. They can be acute, obtuse, or have a special relationships between pairs. Tell your neighbor the difference between acute and obtuse angles.

The Scenario The Riverside students have been invited to purpose designs for a small park on a rectangular plot of land next to the school. The plot has parallel paths crossing it.

A New Path Juan, Marsha, and Cora decide to include in their design a new path that connects different parts of the park. The path will be diagonal and cross the existing two paths. Here are some options they are considering: Option #1 They numbered the angles in their design. 1 2 3 4 5 6 7 8

More Options: Option #1 Option #2 1 2 1 2 3 4 3 4 5 6 5 6 7 8 7 8 How does 1 change in relation to 2 as the new path moves? Name another pair of angles with the same relationship. Option #3 When the path is moved, how does this affect the relationship between 1 and 4? Name another pair of angles with the same relationship. Describe the relationship between 1 and 8. Describe the relationship between 1 and 5. 1 2 3 4 5 6 7 8

Your Turn: Supplies: Activity Sheet: Parallel Lines & Transversals Ruler Protractor Pencil