Exploring Congruent Angles and Angle Bisectors

Objective:

Students will be able to identify congruent angles and understand the concept of angle bisectors by drawing and classifying angles accurately.

Assessment:

Students will be assessed through a worksheet where they need to identify and draw pairs of congruent angles, as well as demonstrate understanding of angle bisectors by accurately bisecting given angles.

Key Points:

• Definition of congruent angles and how to identify them

• Understanding the concept of angle bisectors

• Drawing and classifying angles accurately

• Identifying common misconceptions about congruent angles

Opening:

• Show two angles that look the same and ask students if they know what it means for angles to be congruent

• Engage students with a hands-on activity where they match pairs of congruent angles

Introduction to New Material:

• Explain the definition of congruent angles and show examples

• Introduce angle bisectors and demonstrate how they divide angles

• Address the common misconception that angles need to look the same to be congruent

Guided Practice:

• Provide guided examples for students to identify and draw congruent angles

• Scaffold questioning from simple identification to more complex angle bisector problems

• Monitor student performance by circulating the classroom and offering support as needed

Independent Practice:

• Instruct students to draw and classify different sets of congruent angles

• Assign tasks where students need to identify and draw angle bisectors accurately

• Provide clear expectations for completion and accuracy of the work

Closing:

• Have students share their drawings and explanations of how they identified and classified congruent angles

• Summarize the key points about congruent angles and angle bisectors

Extension Activity:

Encourage early finishers to create their own examples of congruent angles and challenge a partner to identify and draw their own angle bisectors.

Homework:

For homework, students can complete a worksheet identifying congruent angles in everyday objects at home and drawing angle bisectors.

Standards Addressed:

• CCSS Standard: G-CO.A.2 - Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs.

• CCSS Standard: G-CO.A.2 - Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.