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OBJECTIVE - G.GPE.B.5

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

INTERPRETATION OF OBJECTIVE - G.GPE.B.5

This objective is looks at parallel and perpendicular lines on the coordinate grid. We extend the relationship to include their slope relationships. Knowing that parallel lines have equal slopes and perpendicular lines have negative reciprocal slopes allows us to further analyze geometric shapes to determine what they are and what properties they have.

SKILLS

(1) The student will be able to prove that parallel lines have congruent slopes and its converse.

(2 The student will be able to prove that perpendicular lines have negative reciprocal slopes and its converse.

(3) The student will be able to determine the slope of a line.

(4) The student will be able to determine whether two slopes represent parallel or perpendicular relationships.

(5) The student will be able to classify geometric shapes using slopes and/or distances.

THE BIG IDEA

Slopes tell us a lot of information about geometric shapes. Parallel and perpendicular relationships occur in many geometric shapes such as the parallelogram family. Determining slope helps us classify shapes more specifically.

TRAPS & PITFALLS

The ability to understand and recognize negative reciprocal is difficult to students. So many students use negative slopes or reciprocal slopes as perpendicular slopes.... instead of negative reciprocal slopes.

Unfortunately the weak algebra skills hurt them here as well because often you need to transform the equation into a particular form to find the slope and this process often brings errors.

Also classifying quadrilaterals is very difficult when the coordinates are not actual numbers but use variables. This is very abstract for them and they struggle to make sense of size and relationship.

PAST CONNECTIONS

Parallel and perpendicular relationships are not new to students they have been using these concepts in different ways over the years but it is here that we connect it directly to slope.

FUTURE CONNECTIONS

Parallel and perpendicular relationships are everywhere.... tangent lines... derivatives.... quadrilaterals... etc.. This objective sets up another opportunity to strengthen student's understanding of these ideas for the future.

MY REFLECTIONS (over line l)

This objective for the most part is review and most student come with the knowledge of these two slope relationships. The new part is using these two slope relationships to establish or classify various geometric shapes using slope and distance. Students feel comfortable on the grid counting things out but when we use variables for coordinates instead of values they start to struggle. I make this transition slowly beginning with basic shapes and easy coordinates.