Application of Special Segments and Points of Concurrency

If D is the orthocenter, what type of segments are drawn?

• meidans

• altitudes

• angle bisectors

• perpendicular bisectors

Find the measures of segments ZG and ZL.

• mZG=28 and mZL=112

• mZG=56 and mZL=84

• mZG=56 and mZL=112

• mZG=28 and mZL=84

If S is the incenter, what type of segments are drawn?

• medians

• angle bisectors

• perpendicular bisectors

• altitudes

If Z is the centroid, what type of segments are drawn?

• angle bisectors

• perpendicular bisectors

• altitudes

• medians

The point of concurrancy is a ​ (a)   .

• circumcenter

• incenter

• centroid

• orthocenter

Refer to the diagram of △ABC

with its perpendicular bisectors and angle bisectors added and the points of intersection labeled.

Complete each statement. Drag the correct point into each box to label the correct point of concurrency.

Point ​ (a)   represents the point of concurrency of angle bisectors.

Point ​ (b)   represents the point of concurrency of perpendicular bisectors.

• E

• J

• H

• I

• A

• K

• B

• C

• D

• G

Tags

G.CO.12

The point of concurrency for the 3 perpendicular bisectors of one triangle is called the ​ ​ ​ (a)   . The point of concurrency for the 3 medians inside of one triangle is called the ​ ​ (b)   . The point of concurrency for the 3 angle bisectors inside of one triangle is called the ​ (c)   . The point of concurrency for the 3 altitudes inside of one triangle is called the ​ (d)   .

• circumcenter

• centroid

• incenter

• orthocenter

Match the following point of concurrency with the segments that form them:

• medians

• orthocenter

• angle bisectors

• centroid

• perpendicular bisectors

• incenter

• altitudes

• circumcenter

The​ (a)   divides each median into two sections at a 2:1 ratio

• orthocenter

• circumcenter

• incenter

• centroid

The point of concurrancy is a ​ (a)   .

• circumcenter

• incenter

• centroid

• orthocenter