Students will be able to identify and differentiate angles on and inside a circle, apply the Chord/Tangent Angle Theorem, and utilize the Intersecting Chords Angle Theorem.
Students will complete a worksheet where they need to identify angles on and inside a circle, solve problems using the Chord/Tangent Angle Theorem, and prove angles congruent using the Intersecting Chords Angle Theorem.
Angles on a circle: When the vertex is on the edge of the circle.
Angles inside a circle: When the vertex lies anywhere inside the circle.
Chord/Tangent Angle Theorem: [𝛼 = 𝛽] when two chords intersect inside a circle.
Intersecting Chords Angle Theorem: [AB * CD = BC * AD] when two chords intersect inside a circle.
Show a picture of a circle with various angles marked and ask students to discuss what they notice about the angles on and inside the circle
Pose the question: "How are angles on a circle different from angles inside a circle?"
Explain the definitions of angles on and inside a circle
Demonstrate the Chord/Tangent Angle Theorem and solve a sample problem
Common misconception: Students might confuse angles inside the circle with angles outside the circle if they are not clear on the definitions
Provide examples of angles on and inside a circle for students to practice identifying
Guide students through applying the Chord/Tangent Angle Theorem with scaffolded questioning
Monitor student performance by circulating the room, offering support, and providing feedback
Assign a set of problems requiring students to identify angles on and inside a circle, apply the Chord/Tangent Angle Theorem, and use the Intersecting Chords Angle Theorem
Students should show all work and explanations of their solutions
Have students share one key concept they learned about angles on and inside a circle
Summarize the differences between the Chord/Tangent Angle Theorem and the Intersecting Chords Angle Theorem
Challenge students to create their own scenarios where they apply the Chord/Tangent Angle Theorem or the Intersecting Chords Angle Theorem
For homework, students will be asked to find real-world examples of angles on and inside a circle, take pictures, and annotate the angles identified.
CCSS.MATH.CONTENT.HSG-C.A.2: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.