Special Segments of Triangles

Given the pictures and markings, categorize each picture.

Label how each point of concurrency is created.

The centroid cuts each median into ​ (a)   segments.  The shorter segment is ​ (b)   the length of the entire segment. The longer segment is​ (c)   of the entire length.

Given the information & that $$BF=39$$ , find each measure.

$$PD=$$ ​ ​ (a)  

$$CD=$$ ​ (b)  

Given the information & that $$BF=39$$ , find each measure.

$$FP=$$ ​ ​ (a)  

$$BP=$$ ​ (b)  

Given the information & that $$BF=39$$ , find each measure.

$$PA=$$ ​ ​ (a)  

$$EA=$$ ​ (b)  

Given that $$Z\$$ is the incenter, and $$MZ=12,\ YI=18,\ NZ=6.$$ Find the following measures.

$$ZR=$$ ​ (a)  

$$YZ=$$ ​ (b)  

$$MR=$$ ​ (c)  

Name the point of concurrency shown.

10. What type of lines are shown?

Use the Perpendicular Bisector Theorem to find $$DC$$ .