Exploring Same Side Interior Angles

Objective:

Students will be able to identify, define, and calculate same side interior angles, as well as apply the Same Side Interior Angles Theorem and its converse.

Assessment:

Students will be given a worksheet with various pairs of angles formed by parallel lines and a transversal. They must identify the same side interior angles, determine if they are supplementary, and justify their answers.

Key Points:

• Definition: Same side interior angles are two angles that are on the same side of the transversal and on the interior of (between) the two lines.

• Theorem: Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.

• Converse: Converse of the Same Side Interior Angles Theorem: If two lines are cut by a transversal and the same side interior angles are supplementary, then the lines are parallel.

• Formula: Supplementary angles add up to 180 degrees.

Opening:

• Engage students with a real-life scenario involving parallel lines and a transversal.

• Pose the question: "Have you ever noticed specific angle relationships when lines are intersected by another line?"

Introduction to New Material:

• Define same side interior angles and illustrate with diagrams.

• Explain the Same Side Interior Angles Theorem and its converse.

• Anticipate misconception: Students might confuse same side interior angles with other angle relationships formed by parallel lines and a transversal.

Guided Practice:

• Provide examples of identifying and calculating same side interior angles.

• Scaffold questioning from simple identification to determining supplementary angles.

• Monitor student performance through guided questioning and providing feedback.

Independent Practice:

• Assign a worksheet with various scenarios for students to identify and calculate same side interior angles, and apply the theorems to determine parallel lines.

• Encourage students to explain their reasoning for each answer.

Closing:

• Have students share their findings on the relationship between same side interior angles and parallel lines.

• Summarise the key points discussed in the lesson.

Extension Activity:

Challenge early finishers to create their own scenario with parallel lines intersected by a transversal, identify same side interior angles, and determine if the lines are parallel based on their angle calculations.

Homework:

For homework, students should research real-world applications of parallel lines and transversals, and write a paragraph explaining how understanding same side interior angles can be useful in practical situations.

Standards Addressed:

• CCSS Standard: G-GPE.B.5 (Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems)

• CCSS Standard: G-GPE.B.5 (Prove the slope criteria for perpendicular lines and use them to solve geometric problems)