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**Standard(s): **
[MA2019] GEO-19 (9-12) 32 :

*Example: Find the equation of a line parallel or perpendicular to a given line that passes through a given point.*

32. Use coordinates to prove simple geometric theorems algebraically.

[MA2019] GEO-19 (9-12) 33 : 33. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

The challenge of programming robot motion along segments parallel or perpendicular to a given segment leads to an analysis of slopes of parallel and perpendicular lines and the need to prove results about these quantities (G-GPE.B.5). MP.3 is highlighted in this topic as students engage in proving the criterion for perpendicularity and then extending that knowledge to reason about lines and segments. This work highlights the role of the converse of the Pythagorean theorem in the identification of perpendicular directions of motion (G-GPE.B.4). In Lesson 5, students explain the connection between the Pythagorean theorem and the criterion for perpendicularity (G-GPE.B.4). Lesson 6 extends that study by generalizing the criterion for perpendicularity to any two segments and applying this criterion to determine if segments are perpendicular.

In Lesson 7, students will recognize when a line and a normal segment intersect at the origin. Lesson 8 concludes Topic B when students recognize parallel and perpendicular lines from their slopes and create equations for parallel and perpendicular lines. The criterion for parallel and perpendicular lines and the work from this topic with the distance formula is extended in the last two topics of this module as students use these foundations to determine the perimeter and area of polygonal regions in the coordinate plane defined by systems of inequalities. Additionally, students study the proportionality of segments formed by diagonals of polygons.