Students will be able to apply the Angle Bisector Theorem to identify and solve proportions within triangles.
Students will demonstrate mastery of the objective by completing a worksheet containing various triangles where they will identify angle bisectors, determine proportional segments, and solve for missing side lengths using the Angle Bisector Theorem.
Understand the Angle Bisector Theorem: If a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the lengths of the other two sides.
Identify angle bisectors within triangles
Solve for proportional segments within triangles
Apply the Angle Bisector Theorem to find missing side lengths in triangles
Angle Bisector Theorem: If a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the lengths of the other two sides.
Engage students by asking: "How can we use angle bisectors to find proportional segments within a triangle?"
Explain the Angle Bisector Theorem and its application
Demonstrate how to identify and work with angle bisectors in triangles
Common misconception to anticipate: Students may confuse angle bisectors with medians or altitudes of triangles
Provide examples of triangles where students can identify angle bisectors
Scaffold questioning from simple to complex to deepen understanding
Monitor student performance by circulating the classroom and providing guidance as needed
Assign a worksheet with various triangles for students to practice identifying angle bisectors and solving for proportional segments
Behavioral expectations: Work quietly, show all work, and ask for help when needed
Summarise key concepts learned by discussing how the Angle Bisector Theorem helps us understand proportions within triangles
For early finishers, create a task where they can explore real-world examples of angle bisectors in architecture or design
Provide a homework activity where students need to find and sketch examples of angle bisectors in everyday objects or situations
CCSS.MATH.CONTENT.HSG.CO.C.9: Prove theorems about triangles, including the Angle Bisector Theorem and its converse.