Construcing a 30° Angle and Properties of Rhombi

Explore the entire construction in the app above, then use the GeoGebra tools to draw the segments and . What geometric figure is obtained? Why? (Use the Undo and Redo buttons at the top right of the toolbar, or refresh the browser page to delete possible objects you have created but that are not useful or correct).

Now draw segments and . What do they represent for the polygon created previously?

Describe the properties of the diagonals of a rhombus.

Consider the triangle . What type of triangle is it? Explain why you classified it as such.

Complete the following sentence. Let be the point of intersection of and . Then _________ and the triangle is a right triangle with one side __________ the other, therefore the angle measures ___________ .

If a statement is false, correct it to make it true, or provide a counterexample.

1. If a parallelogram has two congruent consecutive sides, therefore it is a rhombus.
2. Some rhombi are rectangles.
3. A quadrilateral whose diagonals are perpendicular to each other is a rhombus.
4. The diagonals of a rhombus are congruent.
5. A rhombus is a figure symmetrical with respect to one of its diagonals.
6. A rhombus is a figure symmetrical with respect to the point of intersection of its diagonals.
7. A rhombus has two pairs of congruent sides.
8. The sum of all the interior angles of a rhombus is equivalent to 2 right angles.
9. In every rhombus the minor diagonal is the same length as the side.