Performance Task: Exploring Triangle Congruence with SSS

Draft Performance Task: Exploring Triangle Congruence with SSS

Teacher Guide

Standards and Skills

Common Core Standard:
G.CO.B.7 - Use the criteria for triangle congruence (SSS, SAS, ASA, AAS, and HL) to prove that two triangles are congruent.

Skills Taught:

  • Understanding the SSS (Side-Side-Side) congruence criterion for triangles

  • Collaborating in groups to solve geometric problems

  • Applying geometric reasoning to prove congruence in triangles

Task Description

Students will work in groups to explore and demonstrate the SSS (Side-Side-Side) postulate for triangle congruence. Each group will create a presentation to explain their findings while solving a multi-step problem that incorporates the SSS criterion.

Task Delivery

Introduction (10 minutes)

  1. Begin with a Review:

    • Refresh students on postulates and theorems related to triangle congruence, focusing on SSS.

    • Discuss why understanding triangle congruence is important in real-world applications such as engineering and architecture.

Group Exploration (30 minutes)

  1. Divide Students into Groups:

    • Form groups of four students. Assign roles within each group (e.g., leader, recorder, presenter, verifier).

  2. Triangle Congruence Investigation:

    • Each group will use rulers, compasses, and colored pencils to construct triangles with given side lengths. Choose three sets of lengths where they can create two triangles that demonstrate SSS congruence.

Problem Solving (40 minutes)

  1. SSS Challenge:

    • Each group is tasked with solving the following problem:

      • Problem Statement: Construct two triangles, △ABC△ABC and △DEF△DEF, where the sides of △ABC△ABC are 5 cm5 cm, 7 cm7 cm, and 10 cm10 cm, and the sides of △DEF△DEF are 5 cm5 cm, 7 cm7 cm, and 10 cm10 cm. Prove the triangles are congruent using SSS and label all corresponding sides and angles accurately.congruent using SSS and label the corresponding sides and angles.

    • Groups must also include a real-world example of where SSS could be applied in design.

Presentation Preparation (20 minutes)

  1. Create a Presentation:

    • Develop a visual presentation (posters, digital slides) that includes:

      • Diagrams of the triangles constructed

      • Step-by-step justification of triangle congruence using SSS

      • A paragraph explaining the real-world application chosen.

Materials Needed

  • Rulers and compasses

  • Colored pencils

  • Poster boards or digital presentation tools (e.g., Google Slides)

  • A clear problem statement and answer sheet with space for notes

Student Directions

Performance Task: Exploring Triangle Congruence with SSS

Objective: Explore and demonstrate the SSS triangle congruence through construction, justification, and presentation.

Steps:

  1. Review and Form Groups

    • Listen to the introduction and get into your assigned groups of four.

  2. Investigate Triangle Congruence

    • Each group member will take on a specific role.

    • Discuss how you will construct triangles based on the set lengths provided.

  3. Construct Triangles

    • Using rulers and compasses, construct triangles that meet the requirements of the problem statement.

  4. Solve the SSS Challenge

    • Work together to prove that the two triangles are congruent using the SSS criteria.

    • Make sure to label all corresponding sides and angles.

  5. Real-World Application

    • Identify a real-world scenario where the SSS postulate is important.

  6. Prepare Presentations

    • Compile your finding into a presentation format. Ensure clarity in the explanations for each segment of your work.

  7. Present Your work

    • Share your findings with the class. Be ready to answer questions from your peers.

Assessment Criteria

Grading Rubric (10 Points)

  • 10 Points: Excellent understanding; all angles and sides correctly labeled; includes relevant real-world application with clear justification of congruence.

  • 8-9 Points: Good understanding; most angles and sides labeled correctly; relevant application discussed but may lack depth.

  • 5-7 Points: Adequate understanding; some errors in labeling; application referenced but lacks detail.

  • 0-4 Points: Limited understanding of SSS; poor presentation; irrelevant application; major errors in triangulation.

Exemplar Solution

A student's group constructs two triangles with sides measuring 5 cm, 7 cm, and 10 cm accurately and demonstrates SSS congruence by clearly labeling the sides and angles. They discuss architecture as an application, explaining how architects ensure structural stability by applying congruence principles.