Quadrilaterals Exploration 2019

Tim Brzezinski, anna.voth, Jan 10, 2019

Properties of Special Quadrilaterals

Table of Contents

  1. Scaffolded Discovery Templates
    1. Copy of Parallelogram Template (Scaffolded Discovery)
    2. Copy of Rectangle Template (Scaffolded Investigation)
    3. Copy of Rhombus Template (Scaffolded Discovery)
    4. Copy of Square Template
    5. Copy of Isosceles Trapezoid Template (Scaffolded Discovery)
    6. Copy of Kite Template: Scaffolded Investigation
  2. Polygon Exterior Angle Sum
    1. Polygons: Exterior Angles

1.

Scaffolded Discovery Templates

  • 1. Copy of Parallelogram Template (Scaffolded Discovery)
  • 2. Copy of Rectangle Template (Scaffolded Investigation)
  • 3. Copy of Rhombus Template (Scaffolded Discovery)
  • 4. Copy of Square Template
  • 5. Copy of Isosceles Trapezoid Template (Scaffolded Discovery)
  • 6. Copy of Kite Template: Scaffolded Investigation

1.1.

Copy of Parallelogram Template (Scaffolded Discovery)

The applet below contains a quadrilateral that ALWAYS remains a parallelogram. The purpose of this applet is to help you understand many of the geometric properties a parallelogram has. Some of these properties are unique and only hold true for a parallelogram (and not just any quadrilateral). The questions you need to answer are displayed below this applet.
Are opposite sides of a parallelogram congruent?
Are opposite angles of a parallelogram congruent?
Do the diagonals of a parallelogram bisect each other?
Does a diagonal of a parallelogram bisect a pair of opposite angles? If so, how many do?
Are the diagonals of a parallelogram perpendicular?
Are the diagonals of a parallelogram congruent?
Does either diagonal of a parallelogram serve as a line of symmetry? If so, how many?
– anna.voth, Tim Brzezinski

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1.4.

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1.5.

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1.6.

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2.

Polygon Exterior Angle Sum

  • 1. Polygons: Exterior Angles

2.1.

Polygons: Exterior Angles

The exterior angles of a triangle, quadrilateral, and pentagon are shown, respectively, in the applets below. [br][br]You can control the size of a colored exterior angle by using the slider with matching color. [br]Feel free to move the vertices of these polygons anywhere you'd like. [br][br][b]Note:[/b] [br]For the [b]quadrilateral[/b] & [b]pentagon[/b], the last two applets work best if these polygons are kept [b]convex.[/b][br]If you don't remember what this term means, [url=https://www.geogebra.org/m/knnPDMR3]click here for a refresher[/url].
Exterior Angles of a Triangle
Exterior Angles of a Quadrilateral
Exterior Angles of a Pentagon
What do you notice? What is common about the measures of the exterior angles of any one of these polygons?
Do you think what you've observed for the triangle, quadrilateral, and pentagon above will also hold true for a hexagon, heptagon, and octagon? [br][br]Create a new GeoGebra file and do some investigating to informally test your hypotheses!
– Tim Brzezinski

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