Find the perpendicular bisector between the two Lowe's locations by:[br]1) select the perpendicular bisector button [icon]https://www.geogebra.org/images/ggb/toolbar/mode_mirroratline.png[/icon][br]2) and then selecting the 2 blue dots representing the Lowe's stores.
This third red dot represents a different chain. Recall that the perpendicular bisector helps find equidistance between points, in this case the Lowe's stores.[br][br]Your perpendicular bisector should nearly pass through this store. What store do you think this is? Why would they put it here?
The third store is Home Depot!
Construct the 3 Perpendicular Bisectors of each triangle using: [icon]/images/ggb/toolbar/mode_linebisector.png[/icon][br][br]Construct [icon]/images/ggb/toolbar/mode_intersect.png[/icon] the point of concurrency (circumcenter which is the intersection of the three lines) for each triangle.[br][br]Construct the Circumcircle [icon]/images/ggb/toolbar/mode_circle2.png[/icon](center at the circumcenter and passing through the vertices).
The Circumcenter (point of intersection of the 3 perpendicular bisectors) is located __________________.
Construct the 3 Angle Bisectors of each triangle using [icon]/images/ggb/toolbar/mode_angularbisector.png[/icon][br][br]Construct the point of concurrency[icon]/images/ggb/toolbar/mode_intersect.png[/icon] (incenter which is the intersection of the three lines) for each triangle.[br][br]Construct the perpendicular line from the [icon]/images/ggb/toolbar/mode_orthogonal.png[/icon] incenter to one of the sides. Mark the intersection at the right angle where the two lines meet.[br][br]Construct the Incircle [icon]/images/ggb/toolbar/mode_circle2.png[/icon](center at the incenter and the point identified on the last step).
The Incenter (point of intersection of the 3 angle bisectors) is located __________________.
[color=#0000ff]Construct the 3 Medians of each triangle (find the midpoint [icon]/images/ggb/toolbar/mode_midpoint.png[/icon] of each side and connect to the opposite vertex [icon]/images/ggb/toolbar/mode_segment.png[/icon].[/color][br][br]For Triangle ABC, mark the centroid [icon]/images/ggb/toolbar/mode_intersect.png[/icon] (point of concurrency) as point X [icon]/images/ggb/toolbar/mode_showhidelabel.png[/icon] and the intersection on Segment BC as point Y. [br][br]Measure AX [icon]/images/ggb/toolbar/mode_distance.png[/icon][br]Measure XY.[br][br]Calculate 2*XY. What do you notice?[br][br][icon]/images/ggb/toolbar/mode_showhidelabel.png[/icon]
The Centriod (point of intersection of the 3 medians) is located __________________.
Construct the 3 Altitudes of each triangle (Perpendicular from a vertex to the opposite side)[br][br]Construct the point of concurrency (orthocenter: which is the intersection of the three lines) for each triangle.[br][br]
The Orthocenter (point of intersection of the 3 Altitudes) is located __________________.