G-GPE - Domain
Expressing Geometric Properties with Equations
High School Geometry · Common Core State Standards · Common Core 2010
Standard Unwrapping
AI-generated as a starting point — sign in to edit.Vocabulary
coordinatesgeometric theoremsconic sectioncircleparabolaellipsehyperbolaequationcenterradiusfocusdirectrixfocisumdifferencedistances
Skills
- identify (coordinates for geometric figures) #dok1
- define (equation for conic sections) #dok1
- translate (between geometric description and equations) #dok2
- derive (equations of conic sections using coordinates) #dok2
- construct (problems involving properties of coordinates) #dok3
- prove (simple geometric theorems algebraically using coordinates) #dok3
- apply (geometric principles using coordinates for problem-solving in complex situations) #dok4
Learning Targets
- I can define the equation of a circle using the center and radius. #dok1
- I can identify key features of conic sections from equations. #dok1
- I can translate between geometric and algebraic representations of conic sections. #dok2
- I can derive the equations of ellipses and hyperbolas using coordinates. #dok3
- I can apply the coordinate system to solve complex geometric problems. #dok4
Big Ideas
- The use of coordinates in geometry enhances understanding and proving geometric principles algebraically.
- Understanding the relationship between different conic sections and their equations provides a foundation for more advanced geometric and algebraic applications.
Essential Questions
- How can coordinates be used to prove geometric theorems?
- What is the significance of conic sections in geometry?
- How do equations help in representing geometric figures?
- What is the process for deriving the equation of a circle?
- In what ways can geometric concepts be integrated into algebraic equations to solve problems?