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. ______________________