TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Properties of Angles and Segments in Circles (Allow approximately 1 week for instruction, review, and assessment) Enduring Understanding(s) Use the following lesson(s) first to Vocabulary Domain: All circles are similar and that relationships exist introduce concepts/build conceptual Tangent, point of tangency, common tangent Cluster: Understand and apply theorems between angles formed by radii, chords, secants understanding. about circles and tangents. engageny Geometry Module 5, Topic C, Writing in Math/Discussion Identify and describe relationships Lesson 11: Properties of Tangents among inscribed angles, radii, and How many tangents can be drawn from a chords. Include the relationship between point outside a circle, from a point on a circle, Essential Question(s) Use the textbook resources to address central, inscribed, and circumscribed and from a point inside a circle? Explain your How can the properties of circles, polygons, procedural skill and fluency. angles; inscribed angles on a diameter reasoning. lines and angles be useful when solving are right angles; the radius of a circle is Lesson 10.5 Tangents pp.718-725 geometric problems? perpendicular to the tangent where the Use the following resources to deepen radius intersects the circle. students' conceptual understanding of Objective(s): mathematical content and develop their Construct the inscribed and Students will ability to apply that knowledge to circumscribed circles of a triangle, and problems. Identify and describe relationships among prove properties of angles for a tangents and radii; quadrilateral inscribed in a circle. Task(s)
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Properties of Angles and Segments in Circles (Allow approximately 1 week for instruction, review, and assessment) Domain: Cluster: Understand and apply theorems about circles 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. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Enduring Understanding(s) All circles are similar and that relationships exist between angles formed by radii, chords, secants and tangents. Essential Question(s) How can the properties of circles, polygons, lines and angles be useful when solving geometric problems? Objective(s): Students will Identify and describe relationships among tangents and radii; Use the following lesson(s) first to introduce concepts/build conceptual understanding. engageny Geometry Module 5, Topic C, Lesson 11: Properties of Tangents Use the textbook resources to address procedural skill and fluency. Lesson 10.5 Tangents pp.718-725 Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to problems. Task(s) Vocabulary Tangent, point of tangency, common tangent Writing in Math/Discussion How many tangents can be drawn from a point outside a circle, from a point on a circle, and from a point inside a circle? Explain your reasoning.