Understanding SSS Similarity Theorem

Objective:

Students will be able to identify and apply the SSS (Side-Side-Side) Similarity Theorem in triangles to determine if they are similar.

Assessment:

Students will be given a worksheet with various pairs of triangles. They need to determine if the triangles are similar using the SSS Similarity Theorem and provide reasoning for their answers.

Key Points:

• Definition of similarity in triangles based on angles and sides: Two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional.

• SSS (Side-Side-Side) Similarity Theorem: If the corresponding sides of two triangles are proportional, then the triangles are similar.

• Identifying corresponding sides and angles in similar triangles

• Applying the SSS Similarity Theorem in solving problems

• Understanding the concept of proportional sides in similar triangles

• Theorem: SSS Similarity Theorem states that the maximum or minimum values of an optimization equation occur at the vertices of the feasible region – at the points where the boundary lines intersect.

Opening:

• Engage students with a real-life scenario involving similar triangles, such as shadows or scale models

• Ask students: "How can we determine if two triangles are similar?"

Introduction to New Material:

• Explain the concept of similarity in triangles and introduce the SSS Similarity Theorem

• Anticipate misconception: Students may think that all triangles with the same angles are similar, emphasizing the need for proportional sides

Guided Practice:

• Provide examples of pairs of triangles for students to work on together

• Scaffold questioning from simple to complex examples

• Monitor student performance by walking around the class and providing feedback as they work

Independent Practice:

• Assign problems for students to work on individually, applying the SSS Similarity Theorem

• Students need to show their reasoning and calculations for each pair of triangles provided

Closing:

• Have students share their answers and reasoning with the class

• Summarize the key points of the lesson on the board

Extension Activity:

• For early finishers, challenge them to create their own pair of similar triangles and solve for unknown sides and angles using the SSS Similarity Theorem

Homework:

• Homework suggestion: Provide a worksheet with a mix of problems involving similarity in triangles, including using the SSS Similarity Theorem to determine if triangles are similar and solve for unknown values.

Standards Addressed:

• CSS.MATH.CONTENT.HSG.SRT.B.4: Use the definition of similarity of triangles and the SSS similarity criterion to decide if two triangles are similar.

• CSS.MATH.CONTENT.HSG.SRT.B.4: Explain why the criteria for triangle similarity are sufficient to establish the similarity of triangles.