Students will be able to identify and apply the Alternate Exterior Angles Theorem and its converse, proving angles are congruent and lines are parallel.
Students will complete a worksheet where they will identify and solve problems involving alternate exterior angles, providing evidence of their understanding through written explanations.
Definition of Alternate Exterior Angles: Alternate exterior angles are two angles that are on the exterior of land m, but on opposite sides of the transversal.
Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. This can be mathematically expressed as:
If a transversal intersects two parallel lines, then alternate exterior angles are congruent.
Converse of the Alternate Exterior Angles Theorem: If two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel. This can be mathematically expressed as:
If alternate exterior angles are congruent, then the lines are parallel.
Identifying congruent angles and parallel lines
Applying the theorems to solve problems
Introduce the concept of alternate exterior angles using real-life examples such as street intersections.
Pose the question: "How can angles formed by two intersecting lines help us determine if lines are parallel?"
Define alternate exterior angles and explain their relationship in parallel lines with the Alternate Exterior Angles Theorem.
Discuss the Converse of the Alternate Exterior Angles Theorem.
Anticipated misconception: "Thinking that any two angles in the same position are alternate exterior angles."
Provide examples for students to identify and solve alternate exterior angles problems.
Scaffold questioning from simple angle identification to proving lines are parallel using the theorems.
Monitor student performance by circulating the room, checking work, and providing immediate feedback.
Assign a worksheet where students will apply the Alternate Exterior Angles Theorem to solve given problems.
Behavioral expectations include working independently, showing all work, and explaining reasoning.
Have students share their answers and explanations to a few problems with the class.
Summarize the key points of the lesson and revisit the importance of understanding the relationship between alternate exterior angles in determining parallel lines.
For early finishers, provide a challenge where they have to create their own set of parallel lines and transversals, then identify all pairs of alternate exterior angles.
Homework suggestion: Create a set of parallel lines and a transversal, then identify and prove the congruence of alternate exterior angles.
CCSS Standard: G-GPE.B.5
CCSS Standard: G-GPE.B.5