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 angle between line [math]AB[/math] and line [math]FG[/math] to 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).
Consider the triangles [math]GCE[/math] and [math]GCD[/math].[br]The segments [math]EC[/math] and [math]CD[/math] are ______________ because ______________________ . [br]Also segments [math]EG[/math] and [math]DG[/math] are ___________________ because ______________________ . [br][br]The segment [math]CG[/math] is _______________ between the two given triangles. [br][br]Therefore the triangles [math]GCE[/math] and [math]GCD[/math] are _________________________ because ______________________________ .
Is the previous proof enough to say that line [math]FG[/math] is perpendicular to line [math]AB[/math]?[br]Explain your reasoning.
If a statement is false, correct it to make it true, or provide a counterexample.[br][br][list=1][*]Infinitely many perpendicular lines to a given line [i]r[/i] pass through one of its points [i]P.[/i] [/*][*]Given a line [i]r[/i] and a point [i]P [/i]belonging to the line, there always exists at least one line through [i]P[/i] and perpendicular to [i]r.[/i] [/*][*]If two intersecting lines form congruent vertical angles, then the two lines are mutually perpendicular.[/*][*]Two perpendicular lines form 4 straight angles at their point of intersection.[/*][*]The projection of a point onto the line it belongs to is the point itself.[/*][/list]