Understanding Vertical Angles

Objective:

Students will be able to identify, define, and apply vertical angles, as well as prove the Vertical Angles Theorem.

Assessment:

Students will be given a worksheet with various pairs of intersecting lines, and they will need to identify the vertical angles in each pair and prove their congruence using the Vertical Angles Theorem.

Key Points:

• Definition of vertical angles

• Vertical Angles Theorem

• Identifying vertical angles in intersecting lines

• Proving vertical angles are congruent

• Common misconception: Thinking that adjacent angles are always vertical angles

Opening:

• Engage students by displaying a diagram with intersecting lines and ask: "What do you notice about the angles formed by these intersecting lines?"

Introduction to New Material:

• Discuss the definition of vertical angles and provide visual examples

• Explain the Vertical Angles Theorem and how it relates to congruence

• Anticipate misconception: Some students may confuse vertical angles with adjacent angles

Guided Practice:

• Students will work in pairs to identify and label vertical angles in given diagrams

• Scaffold questioning from easier examples to more complex ones

• Monitor student performance by circulating the room and providing guidance as needed

Independent Practice:

• Students will complete a worksheet where they identify and prove the congruence of vertical angles in various scenarios

• Provide clear instructions and examples for reference

• Reinforce the importance of proving congruence using the Vertical Angles Theorem

Closing:

• Have students share their findings on vertical angles with the class

• Summarize the key points of the lesson and have students explain the Vertical Angles Theorem in their own words

Extension Activity:

• For early finishers, have them create their own set of intersecting lines with vertical angles for a classmate to solve

Homework:

• Homework suggestion: Have students find real-world examples of intersecting lines and vertical angles, take a photo, and write a short explanation of how they know the angles are vertical.

Standards Addressed:

• CCSS Standard: G-CO.A.3 - Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

• CCSS Standard: G-CO.A.3 - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.