Geometry, Chapter 5 Test B
Name_____________________
D
B
A
E
A
B
C
D
C
fig. 2
fig. 1
1 – 3 use figure 1
1. Name the perpendicular bisector of ΔABC.
2. Name the altitude from point C.
3. Name BD in ΔABC.
4 – 5 use figure 2
4. Name CD in ΔABC.
5. For what type of triangle will D be the midpoint of AB ?
6. The orthocenter is the point of concurrency of the three altitudes of a triangle. Sketch
the three altitudes and mark the orthocenter in the triangle below. (figure 3)
fig. 3
fig. 4
B
E
A
C
D

7. Given AE bisects DAB. Find ED if CB 12 and CE = 5. (not to scale)
8. Sketch all the midsegments of ABC below.
A
fig. 5
7”
fig. 6
M
C
xo
37o
B
P
48o
24”
9. What is the area of the triangle formed by the midsegments ABC above?
10. Points M & P are midpoints of their respective segments, what is the value of x in
figure 6 above?
11. A triangle has sides measuring 12, and 19, what are the possible measures of the
third side?
12. Sketch a triangle and its perpendicular bisectors, use the perpendicular bisectors to
locate the circumcenter of the triangle. Then Sketch the circle circumscribed about the
triangle.
fig. 7
2x + 7
fig. 8
A
x+3
6x – 4
C
x–1
B
3x + 1
13. Find the value of x from figure 7 above.
14. What values of x will guarantee that AB + AC > BC ?
fig. 9
C
B
36o
55o
D
5’
57o
71
A
B
fig. 10
x’
o
D
A
C
E
15. In figure 9 above which is the longest segment?
16. In figure 10 above what is the length of AD ?
17. Find the coordinates of the point of concurrency
(incenter) of the angle bisectors of the triangle in figure 11.
fig. 10
y = – 2x + 10
y = 2x – 2