Geometry Chapter 6
Angles and stuff
Table of Contents
- 6.1 Polygon Angle Sum
- Sum of the Interior Angles of a Polygon
- Exploring Polygon Angles: Triangle through Octagon
- 6.2/6.3 Properties of Parallelograms
- Parallelogram Template (Scaffolded Discovery)
- Parallelogram Construction Template & Discovery Lab
- Parallelograms
- 6.4 Properties of Rhombuses, Rectangles, and Squares
- Rectangle Properties
- Square Properties
- Rhombus Properties
Sum of the Interior Angles of a Polygon
Use your handout with these directions to discover the formula for finding the sum of the interior angles of any polygon.
1. Complete the table on your handout up to a polygon with [color=#980000][b]8 sides[/b][/color]. As you complete each row, look for patterns in order to predict the sum of the next shape.[br][br]2. Once you complete the octagon, make a [b][color=#980000]prediction[/color][/b] for the measurements of a [color=#980000][b]dodecagon[/b][/color]. Use the slider to check your answer. Were you correct?[br][br]3. If you were asked to calculate the sum of the interior angles of any polygon, you should be able to do it without using this page. Come up with a formula that will work for [b][color=#980000]n[/color][/b] sides. (Hint: Click on the "Show triangles" box for a clue)[br][br]4. Use your formula to predict the sum of the angles of a [color=#980000][b]20-gon[/b][/color] and a [b][color=#980000]30-gon[/color][/b]. Use the slider to check your prediction. If you were incorrect, adjust your formula to make it work.[br][br]5. What is the sum of the angles of a [b][color=#980000]40-gon[/color][/b], [b][color=#980000]45-gon[/color][/b],and a [b][color=#980000]50-gon[/color][/b]. Use the slider to check your prediction. If you were incorrect, adjust your formula to make it work.
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:[br][br][br]1) Are opposite sides of a parallelogram congruent?[br]3) Are opposite angles of a parallelogram congruent?[br]4) Do the diagonals of a parallelogram bisect each other?[br]5) Does a diagonal of a parallelogram bisect a pair of opposite angles? If so, how many do?[br]6) Are the diagonals of a parallelogram perpendicular?[br]7) Are the diagonals of a parallelogram congruent?[br]8) Does either diagonal of a parallelogram serve as a line of symmetry? If so, how many?
Rectangle Properties
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