Quadrilateral Constructions

Introduction

Welcome to Quadrilateral Properties.  During your time here, you will learn about the properties about specific quadrilaterals and use these properties to create constructions of each. 

Task

You will use your massive knowledge of these cute, but fierce quadrilateral figures to prove that "real world" figures are, in fact, parallelograms, rectangles, rhombi, squares, trapezoids, and kites!

Process

Go through the PowerPoint and the quadrilateral properties.  The first four will build upon each other.  The last 

 two have separate properties only to themselves but are similar to the first four.  After each group of properties, you will have to construct each shape given certain features.  Before each construction, review the sites to remember certain details needed for your constructions.  Construct two figures per page on plain white paper and gather them into a portfolio.  You must turn in a running checklist every two days to me for me to make sure you are on schedule.  After going through all properties, you will take a quiz.  The final project will be you finding real life examples of each quadrilateral and proving it is in fact that shape.Portfolio Requirements:Title Page - be creativeTable of Contents - order needs to be checklist, constructions, quiz, and then the projectBind the portfolio in a way that is organized and pages can turn easily.The final project will be a grade on its own, but must be included in the portfolio for its final grade.http://zunal.com/zunal_uploads/files/20150422092902udyva.docxhttp://zunal.com/zunal_uploads/files/20150422111103PygyX.docxhttp://zunal.com/zunal_uploads/files/20150422111436yPeta.pptx

Evaluation

Take this quiz after you have gone through all quadrilateral properties and constructions.

 Make sure you've learned the differences among all quadrilaterals!http://zunal.com/zunal_uploads/files/20150422092638yZyRe.docx

Conclusion

Hope you had a good (and fun) time with this project :)  You were asked to go beyond

 the classroom and find where this lesson could relate to you.  Not only did you find these shape around you, you learned how to prove your reasonings without just believing because you were told.  Take this info and use it in our next unit -  YAY!!!!!

Teacher Page
Make sure your students have a firm grasp on basic constructions before completing this task.  Links for constructions are provided, but they are strictly for review purposes.  This WebQuest is for students to put the properties of quadrilaterals into action.  After they learn how to construct each shape, the students have to prove that a road sign is indeed a rectangle or that a tile on the floor is a rhombus and not just a plain parallelogram.  Students have fun finding the shapes in the "real world."  The trapezoid is the hardest to find.  I tried to not limit the students to just an isosceles trapezoid, even though it is the easiest to prove.
Standards
HSG-CO.C.11. Prove theorems about parallelograms

The students will be able to...
• Analyze geometric diagrams to identify what can and cannot be assumed (e.g. do not assume that angles that appear to be right angles are right angles, quadrilaterals are squares, etc.)
• Prove and apply the theorems related to kites: the diagonals are perpendicular, the diagonal connecting the vertex angles is the perpendicular bisector of the other diagonal, and the vertex angles are bisected by the diagonal
• Prove and apply the theorems related to trapezoids: the consecutive angles between the bases are supplementary, the midsegment is parallel to the bases and is equal in length to the average of the lengths of the bases, and the base angles of an isosceles trapezoid are congruent, and the diagonals of an isosceles trapezoid are congruent
• Prove and apply the theorems and their converses related to parallelograms: the opposite sides and opposite angles are congruent, diagonals bisect one another, and consecutive angles are supplementary
• Prove and apply the theorems related to rhombi: the diagonals are perpendicular bisectors of each other, and the diagonals bisect the angles
• Prove and apply the theorems related to rectangles: the diagonals are congruent, and they bisect each other
• Prove and apply the theorems related to squares: the diagonals are congruent, and they are perpendicular bisectors of each other
Credits
Pictures are from google images and from our online Geometry book: connected.mcgraw-hill.com