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GeoGebraGeoGebra Classroom

Points of Concurrency

Find the perpendicular bisector between the two Lowe's locations by: 1) select the perpendicular bisector button Toolbar Image 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. Your perpendicular bisector should nearly pass through this store. What store do you think this is? Why would they put it here?

Perpendicular Bisectors, Circumcenter, and Circumcircle

Construct the 3 Perpendicular Bisectors of each triangle using: Toolbar Image Construct Toolbar Image the point of concurrency (circumcenter which is the intersection of the three lines) for each triangle. Construct the Circumcircle Toolbar Image(center at the circumcenter and passing through the vertices).

The Circumcenter (point of intersection of the 3 perpendicular bisectors) is located __________________.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Angle Bisectors, Incenter, and Incircle

Construct the 3 Angle Bisectors of each triangle using Toolbar Image Construct the point of concurrencyToolbar Image (incenter which is the intersection of the three lines) for each triangle. Construct the perpendicular line from the Toolbar Image incenter to one of the sides. Mark the intersection at the right angle where the two lines meet. Construct the Incircle Toolbar Image(center at the incenter and the point identified on the last step).

The Incenter (point of intersection of the 3 angle bisectors) is located __________________.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Medians and centriods

Construct the 3 Medians of each triangle (find the midpoint Toolbar Image of each side and connect to the opposite vertex Toolbar Image. For Triangle ABC, mark the centroid Toolbar Image (point of concurrency) as point X Toolbar Image and the intersection on Segment BC as point Y. Measure AX Toolbar Image Measure XY. Calculate 2*XY. What do you notice? Toolbar Image

The Centriod (point of intersection of the 3 medians) is located __________________.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Altitudes and Orthocenters

Construct the 3 Altitudes of each triangle (Perpendicular from a vertex to the opposite side) Construct the point of concurrency (orthocenter: which is the intersection of the three lines) for each triangle.

The Orthocenter (point of intersection of the 3 Altitudes) is located __________________.

Select all that apply
  • A
  • B
  • C
Check my answer (3)