Exploring SAS Similarity Theorem

Objective:

Students will be able to understand and apply the SAS Similarity Theorem to identify similar triangles.

Assessment:

Students will complete a worksheet where they have to determine if the given pairs of triangles are similar using the SAS Similarity Theorem. They will also have to explain their reasoning.

Key Points:

• SAS Similarity Theorem:
  The SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

• SAS Formula:
  If two triangles have corresponding sides in proportion and their included angles are congruent, then the triangles are similar.
  Mathematically, this can be represented as:
  If ∆ABC ~ ∆DEF, then AB/DE = BC/EF = AC/DF and ∠A = ∠D, where ∆ represents a triangle, and the letters represent the vertices and sides of the triangles.

• Understand the SAS Similarity Theorem and its components

• Identify when triangles are similar using the SAS criteria

• Apply the SAS Similarity Theorem to solve problems involving similar triangles

Opening:

• Introduction of the SAS Similarity Theorem and its importance

• Engage students with a real-life scenario involving similar triangles and ask them to discuss why the triangles are similar

Introduction to New Material:

• Explain the SAS Similarity Theorem and provide visual examples

• Discuss the key components of the theorem with emphasis on proportional sides and congruent angles

• Address the common misconception that triangles with equal side lengths are always similar

Guided Practice:

• Provide practice problems for students to work on in pairs

• Scaffold questioning from basic identification of similar triangles to more complex applications of the theorem

• Monitor student progress by circulating the classroom and providing guidance as needed

Independent Practice:

• Assign a set of problems for individual practice to reinforce understanding of the SAS Similarity Theorem

• Students will need to determine if pairs of triangles are similar using the SAS criteria and explain their reasoning

Closing:

• Have students share their findings from the independent practice

• Summarise the key points of the lesson and reiterate the importance of the SAS Similarity Theorem

Extension Activity:

• For early finishers, provide a challenge where they have to create their own pairs of similar triangles and prove their similarity using the SAS Similarity Theorem

Homework:

• Homework suggestion: Create a real-world scenario where students have to identify similar triangles and explain why they are similar using the SAS Theorem

Standards Addressed:

• CCSS.MATH.CONTENT.HSG.SRT.B.4: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.