Understanding the Third Angle Theorem

Objective:

Students will be able to demonstrate understanding of the Third Angle Theorem by identifying and applying it to solve problems involving triangles.

Assessment:

Students will be given a worksheet with various triangle problems where they must apply the Third Angle Theorem to find missing angles.

Key Points:

• Third Angle Theorem: If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles must also be congruent.

• The sum of the three interior angles of a triangle is always 180°

• Identifying and applying the Third Angle Theorem to solve problems

Opening:

• Ask students to think about why the sum of interior angles of a triangle always adds up to 180°.

• Show a picture of two congruent triangles with two angles marked and ask students to predict the measure of the third angle in each triangle.

Introduction to New Material:

• Discuss the concept of the Third Angle Theorem and how it relates to the sum of interior angles in a triangle.

• Common misconception: Students may believe that all triangles have the same angles, which is not true.

Guided Practice:

• Provide examples of triangles and guide students through identifying the missing angles using the Third Angle Theorem.

• Scaffold questioning from simple to more complex examples to ensure understanding.

• Monitor student performance by circulating the classroom and checking for correct application of the theorem.

Independent Practice:

• Students will be given a worksheet with various triangle problems to solve using the Third Angle Theorem.

• Behavioral expectations include showing all work and justifying answers with explanations.

Closing:

• Have students share their answers and explanations for the independent practice problems.

• Summarize the key points of the lesson and check for understanding.

Extension Activity:

• For early finishers, provide a challenge problem where they have to find the missing side lengths of a triangle given the angles.

Homework:

• Homework suggestion: Students will be tasked with creating their own triangle problems that involve applying the Third Angle Theorem.

Standards Addressed:

• CCSS.MATH.CONTENT.HSG.CO.C.10: Prove theorems about triangles, including the Third Angle Theorem.

• CCSS.MATH.CONTENT.HSG.CO.C.10b: Use theorems about triangles to solve problems.