In this lesson, you will use a dynamic geometry sketch to generate multiple figures, and then make conjectures about the resulting patterns.
Open the link Interior Angles of a Polygon. The link will open in a new browser window or tab.
In this sketch, you can change the figure by clicking and dragging any vertex with an orange dot. The sketch will automatically measure the interior angle at each vertex, and then calculate the sum of all of the interior angles for that polygon.
Use the sketch to complete the data in the table. Before recording the sum of the interior angles, be sure to generate at least four different polygons with that number of sides.
Make a table like the one shown below in your notes.
To check your answers, click on each blank.
| Number of Sides | 4 | 5 | 6 | 8 | 10 |
| Sum of Measures of Interior Angles | Interactive button. Assistance may be required. _____ 360° | Interactive button. Assistance may be required. _____ 540° | Interactive button. Assistance may be required. _____ 720° | Interactive button. Assistance may be required. _____ 1080° | Interactive button. Assistance may be required. _____ 1440° |
Now, open the link
Exterior Angles of a Polygon. The link will open in a new browser window or tab.
In this sketch, you can change the figure by clicking and dragging any vertex with an orange dot. The sketch will automatically measure the interior angle at each vertex, and then calculate the sum of all of the interior angles for that polygon.
Use the sketch to complete the data in the table. Before recording the sum of the interior angles, be sure to generate at least 4 different polygons with that number of sides.
Make a table like the one shown below in your notes.
To check your answers, click on each blank.
| Number of Sides | 4 | 5 | 6 | 8 | 10 |
| Sum of Measures of Exterior Angles | Interactive button. Assistance may be required. _____ 360° | Interactive button. Assistance may be required. _____ 360° | Interactive button. Assistance may be required. _____ 360° | Interactive button. Assistance may be required. _____ 360° | Interactive button. Assistance may be required. _____ 360° |
Use the information in the tables to sort the following conjectures into two categories: true conjectures and untrue conjectures.
Drag and drop each conjecture into the correct box. Click the Submit button to see if you have sorted correctly.
For each untrue conjecture, explain why the conjecture is not true.
The measure of any interior angle is always a multiple of 10.
This is untrue because while the sum of the measures is a multiple of 180°, which is also a multiple of 10, the measure of any interior angle could be any positive real number.
The measure of an exterior angle for any polygon is always 360°.
This is untrue because the sum of the measures of the exterior angles is 360°, not the measure of any one exterior angle.
