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Unit Details

​​​​​​​​​​​​​​​​​​​​​​​​Instructions: Rockwood unit details share the timeline, the enduring understanding and the essential questions for each unit.  Click on the standard title to be directed to the information on related standards for the unit.​

 Unit Details

Unit Title
Circles
Unit Number
GEOM10
Course
Geometry
Content Area
Math
Description
Students will discover that all circles are similar and the proportionality of the length of an arc intercepted by an angle to the radius. Students will learn the origin of radians and its role as the constant of proportionality and derive the formula for the area of a sector. In addition, students use their prior algebraic understanding of the quadratic equation and Pythagorean Theorem to find the equation of a circle. Students will understand how to utilize the coordinate plane to determine whether a given point is on a circle.
Timeline
3.5 Week(s)
Enduring Understandings
The equation of a circle is derived from the distance formula. It can be used to prove a point lies on a circle in the coordinate plane.
The ratio of the circumference to the diameter is always pi for any size circle.
Essential Questions
Why are all circles similar?
How can the arc length and area of sector formulas be derived using similarity?
What are radians and how are they derived?
How can the equations of circles be derived using the Pythagorean Theorem?
How can coordinate geometry be used to solve real-life problems?



Additional Unit Resources

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Standard
Standard Component
ECO
  
Define angle, circle, perpendicular line, parallel line, line segment and ray based on the undefined notions of point, line, distance along a line and distance around a circular arc.
  
Derive the equation of a circle.
  
  
Standard
Standard Component
  
Prove that all circles are similar using similarity transformations.
ECO
  
Identify and describe relationships among inscribed angles, radii and chords of circles.
ECO
  
Derive the formula for the length of an arc of a circle.
ECO
  
Derive the formula for the area of a sector of a circle.
ECO
  
Use coordinates to prove geometric theorems algebraically.