A Quartet of Quadrilaterals: A First Exploration

Mark Cloud, Mar 24, 2021

Looking at some quadrilaterals

Table of Contents

  1. Introduction
    1. Overview
  2. Quadrilaterals
    1. Explore: Parallelogram
    2. Reflection: Parallelogram
    3. Explore: Rhombus
    4. Reflection: Rhombus
    5. Explore: Rectangle
    6. Reflection: Rectangle
    7. Explore: Square
    8. Reflection: Square
  3. Conclusion
    1. Reflect, Summarize and Synthesize

1.

Introduction

  • 1. Overview

1.1.

Overview

Here are four types of quadrilaterals. [br][br]For each one, move the blue points and make observations about what happens. Take notes on what you see and what you wonder. [br][br]Here are just some of the many things you could explore:[br][br]What do I notice about the side lengths?[br]What happens to the lengths of the sides when a blue point is moved? [br]What do I notice about the angle sizes?[br]What happens to the angle sizes when a blue point is moved? [br]Is the quadrilateral convex or concave? Can this change by moving a blue point?[br]Is the shape equilateral? equiangular? regular? Can this change by moving a blue point? [br]Can a shape be in more than one category ([i]i. e. [/i]a rhombus AND a rectangle)?[br][br]There are many more things you might observe. What can you discover? [br]
– Mark Cloud

2.

Quadrilaterals

  • 1. Explore: Parallelogram
  • 2. Reflection: Parallelogram
  • 3. Explore: Rhombus
  • 4. Reflection: Rhombus
  • 5. Explore: Rectangle
  • 6. Reflection: Rectangle
  • 7. Explore: Square
  • 8. Reflection: Square

2.1.

Explore: Parallelogram

What to do
Move any of the blue points.[br][br]What do you notice? What do you wonder? [br]Are there characteristics that stay the same? Are there things that change?[br][br]Record your thoughts below.
Observations
What do you notice about the sides of the parallelogram?
What do you notice about the angles of the parallelogram?
What other things do you notice about the parallelogram?
– Mark Cloud

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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3.

Conclusion

  • 1. Reflect, Summarize and Synthesize

3.1.

Reflect, Summarize and Synthesize

You just created a lot of polygons that were in different categories. Do some compare and contrast among all the shapes you explored.
What were the characteristics that all of these shapes had in common?
List the differences that they had. For example what makes a rhombus different than a rectangle? Why are rectangles not just parallelograms?
What are the characteristics that are needed for a quadrilateral to be a square? [br]
What do you wonder about?
– Mark Cloud

Information