Download Geometry Points of Concurrency HW Worksheet Name: For

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
̅̅̅̅ = 10, 𝐶𝐹
̅̅̅̅ = 12.
6. D is the centroid of ∆ABC, ̅̅̅̅
𝐴𝐸 = 12, 𝐴𝐷
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. _______________
For Problems 22-24 State a point of concurrency that would help solve each of the problems below. Then state how
you would find that point of concurrency.
22. This rectangle represents the Jones’ lot. The non-shaded triangular region represents
their backyard. The Jones’ want to build the largest possible circular pool in their back
yard, how would you determine the location of the pool’s center?
Merry-go-round
23. The Smith Construction Company has been hired to install a new water fountain at
Winstonian Park. They would like to find the best location for the fountain so that the
walking distance from each of the three main pieces of playground equipment is the same.
How would they determine this point?
24. You are a sculptor and have just completed a large metal mobile. You want
to hang this mobile, made of a flat triangular metal plate, in the State Capitol.
This triangular piece will hang so that it will be suspended with the triangular
surface parallel to the ground. How would you locate the point where the
mobile will balance?
Name the point of concurrency shown for the bold triangle.
25. ____________________
26. __________________
Swing
27. ______________________
See-Saw