Parallelogram
Task
Create a parallelogram and change it by dragging the vertices of the figure. Explore how the values of the sides and angles are changing.
Explore the construction and learn how to discover properties of parallelograms with GeoGebra Geometry. Then try it yourself by following the instructions below.
Explore the construction...
Instructions
Note: If you're using the Mobile App make sure that the chosen Labeling option is New Points Only. You can change this by going to the Settings in the app's menu and then selecting General.
| 1. |  | Select the Line tool and create a line AB by clicking twice in the Graphics View. |
| 2. | | Create a line BC using the Line tool again. Hint: Select point B and then click in the Graphics View to create point C. |
| 3. |  | Activate the Parallel Line tool and create a parallel line to line AB through point C. Hint: Select the line AB and then point C. |
| 4. | | Create a parallel line to line BC through point A using the Parallel Line tool again. |
| 5. |  | Select the Intersect tool and create the intersection point D of the two lines. Hint: Click directly on the intersection point. |
| 6. |  | Activate the Polygon tool and create the parallelogram ABCD by successively selecting all the vertices. Hint: To close your polygon, select the first point again. |
| 7. |  | Select the Show / Hide Object tool and hide the auxiliary lines by selecting the lines. |
| 8. |  | Select a segment using the Move tool and select Show Value. Repeat this for all sides of the parallelogram. Note: In the Mobile App select the More button, then Set caption style and select Value. |
| 9. |  | Display the values of the angles by selecting the Angle tool and selecting the parallelogram. |
| 10. |  | Select the Move tool and explore the properties of your construction. |
Try it yourself...
Instructions (continued)
| 11. |  | Construct the diagonals of the parallelogram using the Segment tool. For the first diagonal select point A and then point C and for the second diagonal select point B and then point D. |
| 12. | | Create the intersection point of the diagonals using the Intersect tool. |
| 13. |  | Select the Distance or Length tool and select each segment of the vertices A, B, C, D and the intersection point E of the diagonals. Hint: Select point A and then point E. Repeat this for points B, C and D. |
| 14. |  | Select the Slope tool and select all four sides of the parallelogram. |
| 15. | | Explore your construction using the Move tool. |