unit summary In this unit, you will explore, prove, and apply important properties of circles that have to do with things like arc length, radians, inscribed angles, and tangents. First, it is important to make sure you're familiar with notation and key terms like radius, diameter, circumference, pi, tangent, secant, and major/minor arcs before you dive into the rest of the circles content. Then we will begin solving equations with arcs, chords, and radii. We will move on to solve problems using algebraic techniques and involving secant and tangent segments. We will focus throughout the unit on real life applications of circle geometry.
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content standards targeted9-12.G-C Circles
·9-12. Understand and apply theorems about circles o 9-12.G-C.1 Prove that all circles are similar.o 9-12.G-C.2 Identify and describe relationships among inscribed angles, radii, and chords.o 9-12.G-C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
o 9-12.G-C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. |
Big ideas
How do we understand circles?
What are the main methods of measuring circles?
How can circle geometry be applied in real life?
How can knowledge of the geometry of triangles be useful with circles?
What are the main methods of measuring circles?
How can circle geometry be applied in real life?
How can knowledge of the geometry of triangles be useful with circles?
Student learning objectives
1. The student will differentiate among the terms related to a circle
2. The student will solve problems involving angles, arcs, or sectors of circles.
3. The student will solve problems involving arcs, chords, and radii of a circle.
4. The student will explore relationships among circles and external lines or rays.
5. The student will solve problems involving properties circles using algebraic techniques.
6. The student will solve problems involving secant segments and tangent segments for a circle.
2. The student will solve problems involving angles, arcs, or sectors of circles.
3. The student will solve problems involving arcs, chords, and radii of a circle.
4. The student will explore relationships among circles and external lines or rays.
5. The student will solve problems involving properties circles using algebraic techniques.
6. The student will solve problems involving secant segments and tangent segments for a circle.