# Geometry: Expressing Geometric Properties with Equations Archive

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• ### MI.Math.Content.HSG-GPE.A.3

(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference…

• ### MI.Math.Content.HSG-GPE.B.4

Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four…

• ### MI.Math.Content.HSG-GPE.B.5

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the…

• ### MI.Math.Content.HSG-GPE.B.6

Find the point on a directed line segment between two given points that partitions the segment in a given…

• ### MI.Math.Content.HSG-GPE.B.7

Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles…

• ### MI.Math.Content.HSG-GPE.A.1

Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to…

• ### MI.Math.Content.HSG-GPE.A.2

Derive the equation of a parabola given a focus and directrix.