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# Geometry: Expressing Geometric Properties with Equations481 questions26 skills

## HSG-GPE.A.1

120 questions7 skills
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

## HSG-GPE.A.2

21 questions1 skill
Derive the equation of a parabola given a focus and directrix.

## HSG-GPE.A.3

172 questions9 skills
Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

## HSG-GPE.B.4

30 questions2 skills
Use coordinates to prove simple geometric theorems algebraically.

## HSG-GPE.B.5

56 questions3 skills
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

## HSG-GPE.B.6

46 questions2 skills
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

## HSG-GPE.B.7

36 questions2 skills
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.