This unit has a close connection with the next unit. For example, a curriculum might merge G.GPE.1 and the Unit 5 treatment of G.GPE.4 with the standards in this unit. Reasoning with triangles in this unit is limited to right triangles; e.g., derive the equation for a line through two points using similar right triangles. Relate work on parallel lines in G.GPE.5 to work on A.REI.5 in High School Algebra I involving systems of equations having no solution or infinitely many solutions. G.GPE.7 provides practice with the distance formula and its connection with the Pythagorean theorem.

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Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ?3) lies on the circle centered at the origin and containing the point (0, 2).
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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).
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Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
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Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
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