Geometry
Points of Concurrency HW Worksheet
Name:________________________
For problems 1-4 identify the point of concurrency shown and what constructions form it:
1. Point: ______________
Formed By: ____________
_____________________
_
2. Point: _______________
Formed By: _____________
______________________
_
3. Point: _______________
Formed By: _____________
______________________
_
4. Point: _______________
Formed By:_____________
______________________
_
5. Point G is the centroid of ∆ABC. ̅̅̅̅
𝐴𝐷 = 8, ̅̅̅̅
𝐴𝐺 = 10, 𝑎𝑛𝑑 ̅̅̅̅
𝐶𝐷 = 18.
Find the length of the given segments:
̅̅̅̅ =_____________
𝐵𝐷
̅̅̅̅
𝐴𝐸 =_____________
̅̅̅̅
𝐴𝐵 =_____________
𝐶𝐺 =_____________
̅̅̅̅
𝐸𝐺 =_____________
̅̅̅̅ =_____________
𝐷𝐺
6. D is the centroid of ∆ABC, ̅̅̅̅
𝐴𝐸 = 12, ̅̅̅̅
𝐴𝐷 = 10, ̅̅̅̅
𝐶𝐹 = 12.
Find the length of each segment:
̅̅̅̅
𝐷𝐺 =____________
̅̅̅̅
𝐴𝐺 =_____________
̅̅̅̅ =___________
𝐷𝐹
̅̅̅̅ =____________
𝐸𝐶
̅̅̅̅
𝐴𝐶 =_____________
7. Which Point of Concurrency is the center of an
inscribed circle as shown below?
____________________________________
8. Which Point of Concurrency is the center of a
circumscribed circle as shown below?
_______________________________
For Problems 9-21, write the letter that corresponds to the point of concurrency in the space provided.
A. Circumcenter
B. Incenter
C. Centroid
D. Orthocenter
9. Which points of concurrency are always inside the triangle? ____________________, __________________
10. Which point of concurrency is always on the vertex of a right triangle? ______________________________
11. Which point of concurrency is always on the midpoint of the hypotenuse in a right triangle? _____________
12. Which points of concurrency are always outside of an obtuse triangle? _______________, ______________
13. Which point of concurrency is the center of gravity in a triangle? ___________________________
14. Which point of concurrency is equidistant from every vertex? _____________________________
15. The three altitudes of a triangle intersect at the ____________________.
16. The three medians of a triangle intersect at the ____________________.
17. The three perpendicular bisectors of a triangle intersect at the ____________________.
18. The three angle bisectors of a triangle intersect at the ____________________.
19. It is equidistant from the three vertices of the triangle. _______________
20. It is equidistant from the three sides of the triangle. _________________
21. It divides each median into two sections at a 2:1 ratio. _______________
mobile will balance?
Name the point of concurrency shown for the bold triangle.
22. ____________________
23. __________________
24. ______________________