Pre-AP Geometry – Homework 5



Pre-AP Geometry Name ______________________

Worksheet: Special Segments & Pts of Concurrency Date __________ Period ____

Fill in the Blank:

1. In a triangle, a perpendicular bisector is __________________ to a side of the triangle

and intersects that side at its ____________________.

2. In a triangle, an angle bisector divides an angle into two congruent ________________.

3. In a triangle, a median connects a ______________ with the _______________ of the

opposite side.

4. In a triangle, an altitude connects a _________________ with the line containing the

opposite side, and is _________________to that line.

Determine if each of the following statements is true or false.

__________ 7. If G is the midpoint of [pic], then [pic] is a median of (EBD.

__________ 8. If [pic], then [pic] is an altitude of both (ECD and (ECG.

__________ 9. If [pic], then [pic] is an altitude of (ECD.

__________ 10. If [pic], then [pic] is a perpendicular bisector of (ECD.

__________ 11. If [pic] is a median of (ECD, then G is a midpoint of [pic].

__________ 12. Each leg of a right triangle is also an altitude of the triangle.

13. Write the equation of the line containing the

altitude of (ABC through vertex B.

14. Write the equation of the median of (ABC

through vertex A.

Fill in the Blank.

15. In a triangle, the point of concurrency of the perpendicular bisectors is called the

______________________.

16. The point of concurrency of the perpendicular bisectors is equidistant from the

______________________.

17. In a triangle, the point of concurrency of angle bisectors is called the ______________.

18. The point of concurrency of the angle bisectors is equidistant from the ______________.

19. In a triangle, the point of concurrency of the medians is called the _________________.

20. In a triangle, the point of concurrency of the altitudes is called the ________________.

Fill in the blank with: always, sometimes, or never:

21. A median of a triangle _____________________ has a midpoint as an endpoint.

22. A median of a triangle ______________________ lies outside of the triangle.

23. A perpendicular bisector of a triangle _____________ contains a vertex of the triangle.

24. The angle bisectors of a triangle _________________ intersect at a single point.

25. The circumcenter of a triangle __________________ lies outside the triangle.

26. The centroid of a triangle _____________________ lies outside the triangle.

27. The orthocenter of a triangle ______________________ lies on the triangle.

28. The incenter of the triangle _______________________ lies on the triangle.

Fill in the blank:

29. In an isosceles triangle, the altitude from the _________________ to the

________________ is also a perpendicular bisector, an angle bisector, and a median.

30. In an _______________ triangle, the circumcenter, incenter, centroid, and orthocenter

are the same point.

V is the centroid of (PRT shown to the right.

31. If QV = 3, then QT = _____

32. If VS = 7, then PV = _____

33. QV = 3m – 1 and QT = 7m + 3.

Find the value of m, then find VT. Show work.

34. Using the figure below, Triangle ABC is isosceles and ................
................

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