# Gr. HS Unit: Circles With and Without Coordinates

**LESSON UNIT**

**LESSON PLANS**

- Proving Similar Circles (DOCX)
- Defining Radian Measure and Arc Length (DOCX)
- Coordinate Proofs with Circles (DOCX)

**LESSON SEEDS**

- Exploring Circumscribed Circle (DOCX)
- Equations of Circles (DOCX)
- Inscribed Angle (DOCX)
- Arcs and Sectors of A Circle (DOCX)

### UNIT OVERVIEW

In this unit students prove basic theorems about circles, such as a tangent line is perpendicular to a radius, inscribed angle theorem, and theorems about chords, secants, and tangents dealing with segment lengths and angle measures. They study relationships among segments on chords, secants, and tangents as an application of similarity. In the Cartesian coordinate system, students use the distance formula to write the equation of a circle when given the radius and the coordinates of its center. Given an equation of a circle, they draw the graph in the coordinate plane.

**Essential Questions:**

- How is visualization essential to the study of geometry?
- How does the concept of similarity connect to the study of circles?
- How does geometry explain or describe the structure of our world?
- How do relationships between angles and arcs enhance the understanding of circles?
- How can reasoning be used to establish or refute conjectures?
- What is the role of algebra in proving geometric theorems?

A question is essential when it stimulates multi-layered inquiry, provokes deep thought and lively discussion, requires students to consider alternatives and justify their reasoning, encourges re-thinking of big ideas, makes meaningful connections with prior learning, and provides students with opportunities to apply problem-solving skills to authentic situations.

##### Unit Lesson

Additional information such as Teachers Notes, Enduring Understandings,Content Emphasis by Cluster, Focus Standards, Possible Student Outcomes, Essential Skills and Knowledge Statements and Clarifications, and Interdisciplinary Connections can be found in this Lesson Unit.