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.
Complete the construction by drawing segment [math]CD[/math].[br]Consider the triangle [math]ACD[/math] and describe its characteristics, showing why angle [math]CAD[/math] measures [math]60°[/math].[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).
Calculate the length of the height relative to side [math]BC[/math] of the triangle below, using the available information.[br][br][br][img]data:image/png;base64,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[/img]
Describe the properties of triangles with interior angles [math]30°-60°-90°[/math].
A very creative architect decides to tile a kitchen countertop using [math]1000[/math] triangular tiles. Each tile has one side measuring [math]12[/math] cm, another side meausring [math]6[/math] cm, and the angle opposite the [math]6[/math] cm side is [math]30°[/math]. [br]What is the shape of each tile? Draw it. [br][br]Tiles are sold in boxes, each containing [math]0.5[/math] square meters of tiles . [br]How many boxes must the architect buy to have enough tiles to cover the entire kitchen countertop?
If a statement is false, correct it to make it true, or provide a counterexample.[br][list=1][*]If the hypotenuse of a triangle with angles [math]30°-60°-90°[/math] measures [math]5[/math][i] [/i]m, also one of the legs of the triangle measures [math]5[/math] m.[/*][*]If the base [math]AB[/math] of a triangle with angles [math]30°-60°-90°[/math] measures [math]5[/math] m, the height relative to side [math]BC[/math] splits that side into two segments, each measuring [math]2,5[/math] m.[/*][*]Two triangles with corresponding angles measuring [math]30°-60°-90°[/math] are congruent.[/*][*]An equilateral triangle can be always obtained by mirroring a triangle with angles [br][math]30°-60°-90°[/math][/*][/list]