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

0

This activity is also part of one or more other Books. Modifications will be visible in all these Books. Do you want to modify the original activity or create your own copy for this Book instead?

This activity was created by '{$1}'. Do you want to modify the original activity or create your own copy instead?

This activity was created by '{$1}' and you lack the permission to edit it. Do you want to create your own copy instead and add it to the book?

Quadrilaterals Exploration

Tim Brzezinski, anna.voth, deanna.cullins, Samantha Voorhees, Jan 8, 2018

Properties of Special Quadrilaterals

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

Information

Scaffolded Discovery Templates

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

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.

Use the tools GeoGebra within this applet to investigate the answers to the following questions: 1) Are opposite sides of a parallelogram congruent? 3) Are opposite angles of a parallelogram congruent? 4) Do the diagonals of a parallelogram bisect each other? 5) Does a diagonal of a parallelogram bisect a pair of opposite angles? If so, how many do? 6) Are the diagonals of a parallelogram perpendicular? 7) Are the diagonals of a parallelogram congruent? 8) Does either diagonal of a parallelogram serve as a line of symmetry? If so, how many?

– Tim Brzezinski

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

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. You can control the size of a colored exterior angle by using the slider with matching color. Feel free to move the vertices of these polygons anywhere you'd like. Note: For the quadrilateral & pentagon, the last two applets work best if these polygons are kept convex. If you don't remember what this term means, click here for a refresher.

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?

Font sizeFont size

Very smallSmallNormalBigVery big

Bold [ctrl+b]

Italic [ctrl+i]

Underline [ctrl+u]

Strike

Superscript

Subscript



Font color

Auto

Justify

Align left

Align right

Align center

• Unordered list

1. Ordered list

Link [ctrl+shift+2]

Quote [ctrl+shift+3]

[code]Code [ctrl+shift+4]

Insert table

Remove Format

Insert image [ctrl+shift+1]

Insert icons of GeoGebra tools

[bbcode]

Text tools

Insert Math

Do you think what you've observed for the triangle, quadrilateral, and pentagon above will also hold true for a hexagon, heptagon, and octagon? Create a new GeoGebra file and do some investigating to informally test your hypotheses!