Use compass and ruler to draw on paper the construction described in the app below.
The following app is the same as the previous one, but now includes GeoGebra tools.
Explore the entire construction in the app above, then use the GeoGebra tools to measure the sides of the triangle [math]ABC[/math] and verify the construction numerically.[br][br](Use the [i]Undo [/i]and [i]Redo [/i]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).
Classify triangles based on their sides and angles.
Referring to the construction above, explain why the triangle you obtain is equilateral.
[math]ABC[/math] is an equilateral triangle.[br]On its sides, construct the congruent segments [math]AM\cong BN\cong CP[/math].[br]Show that triangle [math]MNP[/math] is equilateral.
If a statement is false, correct it to make it true, or provide a counterexample.[br][br][list=1][*]Equilateral triangles are concave polygons.[/*][*]Equilateral triangles are also isosceles triangles.[/*][*]The exterior angles of an equilateral triangle are congruent to each other, and their sum is [math]180°[/math].[br][/*][/list]