Compass Vocab - Points of Concurrency

Concurrent

When three or more lines intersect in a single point

Circumcenter - Construction

Perpendicular bisectors

Circumcenter - Properties

• The circumcenter is equidistant from each vertex

• Center of the circumscribed circle

Circumcenter - Example

Cell phone tower being placed in a location equal distance from each surrounding towns

Location of Circumcenter

• Obtuse - outside

• Acute - inside

• Right - midpoint of hypotenuse

Incenter - Construction

Angle bisectors

Incenter - properties

• The incenter is equidistant (perpendicular distance) from each side

• Center of inscribed circle

Incenter - Example

Location for a rest area that is equal distance from 3 highways

Location for Incenter

Always inside the triangle

Centroid - Construction

Medians

Centroid - properties

• Center of gravity

• The centroid breaks each mediano in a 2:1 ratio from each vertex

• Median - connects a vertex to the midpoint (bisects segment into equal lengths)

Centroid - Example

Balancing triangular artwork at once location

Centroid - Location

Always inside a triangle

Orthocenter - Construction

Altitudes

Altitude Properties

• Creates 90 degrees/Perpendicular line

Orthocenter - Example

No real world examples

Orthocenter - Location

• Acute - inside

• Obtuse - outside

• Right - vertex of right angle