Students will be able to identify and calculate inscribed angles in circles, apply the Inscribed Angle Theorem, and the Congruent Inscribed Angles Theorem.
Students will demonstrate mastery of the concept by correctly identifying inscribed angles and their intercepted arcs in a series of circle diagrams.
Definition of Inscribed Angle: An inscribed angle is an angle with its vertex on the circle and whose sides are chords.
Definition of Intercepted Arc: The intercepted arc is the arc that is inside the inscribed angle and whose endpoints are on the angle.
Vertex of an Inscribed Angle: The vertex of an inscribed angle can be anywhere on the circle as long as its sides intersect the circle to form an intercepted arc.
Inscribed Angle Theorem: This theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.
Congruent Inscribed Angles Theorem: This theorem states that if two inscribed angles intercept the same arc (or congruent arcs), then the angles are congruent.
Engage students by asking: "Have you ever noticed how angles inside a circle relate to the circle itself? Let's explore inscribed angles in circles today!"
Define inscribed angles and intercepted arcs
Explain the Inscribed Angle Theorem
Anticipated misconception: Belief that the vertex of an inscribed angle must be at the center of the circle
Provide examples of inscribed angles for students to practice identifying
Scaffold questioning from simple to complex to ensure understanding
Monitor student progress by circulating the room and providing guidance as needed
Assign a worksheet with various circle diagrams requiring identification of inscribed angles and their intercepted arcs
Students will work independently to apply the concepts taught during the lesson
Summarize the key concepts learned about inscribed angles in circles
Ask students to share one new thing they learned today about inscribed angles
For early finishers, challenge them to prove the Inscribed Angle Theorem using their understanding of inscribed angles
Ask students to find examples of inscribed angles in real-life situations and write a short paragraph explaining their findings
CCSS.MATH.CONTENT.HSG-C.A.2: Identify and describe relationships among inscribed angles, radii, and chords.
CCSS.MATH.CONTENT.HSG-C.A.2: Construct the Inscribed Angle Theorem and describe its proof.