Geometry Test – Chapter 5
Name: _____________________________
For problems 1-3, find the value of x. Then, give the theorem or postulate that justifies your answer.
1.
2.
3.
For problems 4-7, find the value of x.
4.
5.
6.
7.
x = ____________
8. Given the figure below, name each of the following segments or rays with relation to ΔABC.
a) BF : _______________________
b) CD : _______________________
c) AG : _______________________
d) EF : _______________________
e) FH : _______________________
9. The park officials want to place a drinking fountain so that it is equidistant
from the tennis court, the playground, and the volleyball court. Which point of
concurrency do they need to find?
a) orthocenter
b) incenter
c) circumcenter
d) centroid
10. Points M, L, and N are the midpoints of each side. Point P is called ?
a) orthocenter
b) incenter
c) circumcenter
d) centroid
11. List the angles of each triangle from smallest to largest.
a) BCD with
b)
12. During lunch, Juan was making triangles with some straws. If he has a 3-in. straw and a 4-in. straw, which
straw can he not use to form a triangle?
A. 5-in. straw
B. 4-in. straw
C. 7-in. straw
D. 6-in. straw
13. Two sides of a triangle have lengths of 12 and 18. The length of the third side can be any number
between _______ and _______.
14. In the segment below, which segment is the longest?
Determine whether AB is a perpendicular bisector, and angle bisector, a median, or an altitude.
15. _______________________
16. ____________________________
17. In the figure below, C is the centroid. Given that KP = 21, JC = 12, and CM = 9. Find the following measures.
a) KC = ____________
b) CN = ____________
c) ML = ____________
18. Answer the following to find the point of concurrency.
a) Graph the triangle with vertices A(0, 0), B(16, 0), C(14, 18).
b) Find the midpoint (M) of each side of the triangle.
AB : M = ___________________ (label point as X)
BC : M = ___________________ (label point as Y)

AC : M = ___________________ (label point as Z)

c) Find the equation and graph each line in y = mx + b form. Show all work.
CX
BZ
d) Algebraically find the intersection of lines CX and AY . Show all work.


e) This point of concurrency is called the what? (circle one)
1) incenter
2) centroid
3) cirmumcenter
4) orthocenter
19. Complete the following proof.
Given: Figure to the right
Prove: m4  m5
Statements
Reasons
1. m4  m2
1.
2. m2  m5
2.
3. m4  m5
3.