Secondary Mathematics
Material Type:
High School
Lesson Plan, Proving Parallelograms
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Education Standards

Proving Parallelograms:Social Media Shape Project

Proving Parallelograms:Social Media Shape Project


This lesson series is designed to teach students how to prove parallelograms by slope, distance and midpoints.  Students will have a performance assessment where they give their shape a personality and bring their shape to life.  They will then prove mathematically that their shape is, indeed, a paralellogram by each of the methods described. 


This lesson is to help give a visual representation to a shape in real life, then to give it a personality.  Once that has been established, students will prove, mathematically, that their chosen shape is a parallelogram.  

This should be a two day project that follows a 3 day lesson series.  These can take place virtually, or face-to-face.  This could be done asynchronously, but are more effective if done together.



Background for Teachers

In this section, explain what teachers need to know before teaching this lesson. This is a great place to include articles, files, and web links that will help teachers research the topic covered in the lesson. Here are some sentence starters that might help you compose this section of your lesson:

  • To teach this lesson, you will need an understanding of proving parallelograms by slope, distance, and calculating midpoints.
  • You will need knowledge about the previously mentioned vocabulary/formulas before teaching this lesson.
  • The following resources can help you teach this topic Proving ParallelogramsTwo-column proof
  • Search the following resources in Utah's Online Library for articles related to this lesson...


Step 1 - Goals and Outcomes

I have found that students tend to enjoy this project much more if they are given creative freedom to interpret the directions however they choose.  Some students keep the project very literal, while others take a more whimsical approach. 

Step 1 Goals and Outcomes

Learning Intentions:

  • Students will be able to understand the properties of quadrilaterals that relate to other geometric definitions and relations (ie. right angles, parallel lines, vertical angles, equilateral, etc.)
  • Students will be able to understand how quadrilaterals are related to one another (ie. all rectangles are also parallelograms.)
  • Students will be able to relate specific the way that specific parallelograms appear in pop culture, art, and as an important part of many jobs or areas of study.

Success Criteria:

  • Students will pick one shape to "give life" to.
  • Students will describe all aspects of their shape. (Either real or ficticious) 
  • Students will create a visual story for their shape usint Adobe Spark, or some other platform.
  • Students will prove mathematically that their shape is a parallelogram by using slope, distance, and midpoints.


Step 2 - Planning Instruction

A review of calculating slope could be beneficial for students who do not have a strong mathematical background.  

Step 2 Planning Instruction

Student Background Knowledge

  • Prior to this lesson, students will need to have an understanding of parallel lines and angles, including appropriate vocabulary. 
  • Students should remember the Pythagorean Theorem, and how it can be used to calculate distance. 

Strategies for Diverse Learners

Some students done well with a quick vocabulary refresher, while other students have struggled with the vocabulary.  I have found that creating a review on Bamboozle really helps the students remember the terms, while making it more of a game.  I have also done a quizlet to help students remember these terms and definitions.  

Step 3 - Instruction

These lessons may require more time, depending on student understanding, and results to formative assessments.  

Step 3 Instruction


  • Files:
    • Students will work as a class through the guided notes provided.
    • Students will complete support assignments utilizing concepts covered.
      • Include opportunities for students to collaborate and restate knowledge.
        • Think-Pair-Share is great for going over materials.
        • Bamboozle, Quizlet and other online game platforms are more effective to review day 1 notes, than simply providing the definitions to each concept.



Step 4 - Assessments

Step 4 Assessments

Students will have a performance assessment for this lesson that includes creating a digital slideshow using Adobe Spark, or some other platform.

Students are in charge of creating a slideshow for a special parallelogram that has been discussed in class (any parallelogram).  They will decide its picture, who its friends are, what it likes or dislikes, favorite things to do, etc.  They are essentailly giving their shape a personality.  Each personality trait should be represented by an original photo, a free use photo, or any other online photo that has been cited correctly.

Once a well-rounded personality has been established, students will then prove, mathematically, that their chosen shape is indeed a parallelogram.  They will prove this by distance, slope and midpoints.  This Proof will be the final page of their presentation.

I have attached a sample project, without a proof (since this shape is a circle).

Be sure to attach rubrics for any assessments included in your lesson using the "Attach Section Resources" button below. Rubric attachments could be screenshots of rubrics created in Canvas, spreadsheets or documents containing rubrics, or rubrics created using the UEN Rubric Tool.


Students with standard accomodations, may require additonal time on assignment, or reduced assignment.  Students who require reduced assignments, could limit the amount of "personality" requirements for their shape.  Bare minimum would be a name, a profile picture for their shape, and each type of proof done correctly.  Additionaly, students would still be expected to cite their source correctly for their main profile page.