Exploring Exterior Angles Theorems

Objective:

Students will be able to understand and apply the Exterior Angle Sum Theorem and the Exterior Angle Theorem to solve problems related to exterior angles of polygons.

Assessment:

Students will be assessed through a worksheet containing various polygon diagrams where they will calculate exterior angles using the theorems learned in class.

Key Points:

• Definition of Exterior Angle: An exterior angle of a polygon is formed by one side of the polygon and the extension of an adjacent side.

• Exterior Angle Sum Theorem: The sum of the exterior angles of a polygon, one at each vertex, is always 360 degrees.

  • Formula: Σ Exterior Angles = 360°

• Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

  • Formula: m∠CAB = m∠A + m∠B

Opening:

• Start with a real-life example of how exterior angles are used in architecture.

• Pose the question: "What do you think happens when you extend a side of a polygon to create an exterior angle?"

Introduction to New Material:

• Discuss the definition of Exterior Angles and provide examples.

• Introduce the Exterior Angle Sum Theorem and Exterior Angle Theorem.

• Common Misconception: Students might confuse interior and exterior angles, clarify the difference.

Guided Practice:

• Work through examples of finding exterior angles in different polygons together.

• Scaffold questioning from easier polygons to more complex ones.

• Monitor student performance by circulating the room and providing support where needed.

Independent Practice:

• Assign a worksheet with various polygon diagrams for students to work on independently.

• The worksheet will include a mix of problems requiring the use of Exterior Angle Sum Theorem and Exterior Angle Theorem.

Closing:

• Have students present their solutions and discuss any challenging problems as a class to summarize the key concepts learned.

Extension Activity:

• For early finishers, provide a set of more complex polygon diagrams to challenge them to apply the theorems in unconventional ways.

Homework:

• Create a set of 5 different polygons and calculate the exterior angles of each using the theorems learned in class.

Standards Addressed:

CCSS.MATH.CONTENT.HSG.CO.C.11: Prove theorems about parallelograms. CCSS.MATH.CONTENT.HSG.CO.C.11: Understand theorems about circles.