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Standards/Math/Massachusetts/G-GPE.B

G-GPE.B

G-GPE Geometry - Expressing Geometric Properties with Equations
G-GPE.A
G-GPE.B
G-GPE.B.4G-GPE.B.5G-GPE.B.6G-GPE.B.7

Use coordinates to prove simple geometric theorems algebraically.

G-GPE.B.4Use coordinates to prove simple geometric theorems algebraically including the distance formula and its relationship to the Pythagorean Theorem. 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).G-GPE.B.5Prove 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).G-GPE.B.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.G-GPE.B.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles (e.g., using the distance formula).
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