Download Mark the picture. Complete the statement with

Unit 3 Review
Multiple Choice. Choose the best answer.
1. The orthocenter is located inside the triangle _________________.
a. Sometimes
b. Always
c. Never
2.Given square MNOP. The perimeter of MNOP is 72cm, NO = 2x + 6. Find x.
a. x = 15
b. x = 12
c. x = 9
d. x = 6
3.The sides of a triangle are 12, 7 and x. Which of the following is a possible value for x?
a. 19
b. 5
c. 8
d. 21
4. E is the midpoint of AC and BD . Choose the true statement.
a. AEB  DEC by ASA
b. AEB  DEC by SAS
c. AEB  CED by ASA
d. AEB  CED by SAS
5.
A
E
B
D
The angle bisectors of a triangle intersect at the:
a. Orthocenter
b. Incenter
c. Centroid
d. Circumcenter
6. Which
a.
b.
c.
d.
C
points of concurrency may lie outside the triangle?
orthocenter and the circumcenter
circumcenter and incenter
centroid and incenter
centroid and orthocenter
7. In CAT ,
C is 54 and T is 36. What is the longest side of the triangle?
a.
CA
b. AT
c. CT
d. cannot be determined
8. In the figure at the right, M is the midpoint of AC . What is BM called?
a.
b.
c.
d.
incenter
median
altitude
angle bisector
A
M
C
B
Complete the statement given that mBAD  mGAE  90
9.
If mBAE  140 , then m4  ____
10.
If mBAG  120 , then mGAF  ____
11.
12.
m2  30 , then m4  ____
If m3  50 , then m6  ____
If
Free Response. Answer completely. Show all work!
13. Use the information in the diagram to solve for x. Show your work.
T
V
4x
8x
U
14. Identify the point of concurrency in each of the drawings.
a.
b.
C
C
G
Centroid
F
A
D
A
E
B
B
15. Point G is the centroid of the triangle. Use the given information to find the length of
each segment.
B
BG = ________________
DG = ________________
D
BE = ________________
BF = 36
E
G
A
6
8
C
F
16. Give the restrictions on the lengths of the third side of the triangle given the lengths of
the other two sides.
a) 22 in, 12, in.
b) 34 m, 19 m.
17. Find the measure of angles x and y.
x=____, y=_____
y
250
500
x
18. State the third congruence (segments or angles) that must be given to prove # ABC # XYZ .
Given: B  Y , AB  XY
a) _____  ______ by ASA
Z
C
b) _____  ______ by SAS
A
B
Y
X
Identify the inverse, converse, and contrapositive of each conditional statement.
19
If it rains, then it is cloudy.
Inverse:
Converse:
Contrapositive:
Decide if the conditional and converse are true. If they are true, then write the Bi-conditional statement. If the
converse is false, provide a counterexample
20.
If two angles are vertical, then they are congruent.
Inverse:
Converse:
Contrapositive:
Decide if the conditional and converse are true. If they are true, then write the Bi-conditional statement. If the
converse is false, provide a counterexample.
Determine if statement (3) follows statements (1) and (2) by the Law of Detachment or the Law of
Syllogism. If the statement is invalid, simply write invalid.
21.
22.
(1) If a student is enrolled at Topeka High School, then the student has an ID number.
(2) Todd Rutland is enrolled at Topeka High School.
(3) Todd Rutland has an ID number.
(1) If an angle measures 123  , then it is obtuse.
(2) m C = 123 
(3)
C is obtuse
23.
(1) If you like pizza with everything, then you’ll like Jimmy’s pizza.
(2) If you like Jimmy’s pizza, then you are a pizza connoisseur.
(3) If you like pizza with everything, then you are a pizza connoisseur.
24.
(1) If your car needs more power, then use Power Pack Motor Oil.
(2) Marcus uses Power Pack Motor Oil.
(3) Marcus needs more power in his car.
Find the indicated length for each problem.
25. Given YP  24 and PO =10.
M
Find PM  _______________.
P
N
Y
Z
26. The angle bisectors of ABC meet at point P.
O
B
Given CR  24 and PC  30 .
Q
Find QP  _______________.
P
C
S
A
R
B
27. The perpendicular bisectors of ABC meet at point D.
Given AC  48 and GD  7 .
E
F
Find BD  _______________.
D
A
G
C
Point X is the centroid of ABC . Given CE  48 , AX  24 , and XD  10 .
Find the indicated lengths.
B
28. CX  _______________
29.
XF  _______________
30. BX  _______________
E
31. BD = _______________
F
X
A
D
C
Set up an equation and find the value of x. Explain your reasoning for the set up of each equation.
If you move any angle, show where it moved and explain how you moved it.
32.
Equation:____________________
Reason:________________
x = ______________
8(x – 9)°
112°
33.
Equation:____________________
Reason:________________
x = ______________
(5x + 7)°
(7x – 31)°
34.
Equation:____________________
(10x – 10)°
Reason:________________
x = ______________
(6x – 2)°
35. Find the value of x.
X=
50º
25+x0
3x-18º
Which of the following can be the sides of a triangle?
a)3,4,5
b)7,7,7
c)9,9,18
36. Give the restrictions on the lengths of the third side of the triangle given the lengths of the other two sides.
a) 21 in, 20 in.
b) 40 m, 30 m.
37.
Identify the property that can be used to prove these triangles congruent. Write the congruence statement.
A
B
E
C
D
E
V
A
38.
C D
F
Based on the triangle below, list the sides of the triangle from least to greatest.
C
700
A
450
650 B
39. Based on the triangle below, list the angles of the triangle in order from least to greatest
B
18
21
A
C
13
40.
a)
b)
c)
d)
e)
f)
Fill in the blank with the appropriate point of concurrency.
The _______________________ is the point where all the angle bisectors intersect.
The _______________________ is the point where all the altitudes intersect.
The _______________________ is the point where all the perpendicular bisectors intersect.
The _______________________ is the point where all the medians intersect.
The _____________ or ___________ are always inside the triangle.
The _____________ or ___________ can be outside the triangle.
41. Point G is the centroid of the triangle. Use the given information to find the length of each segment.
B
a) BG = ________________
b) BD = ________________
D
c) DG = ________________
E
7
G
5
A
42. List the sides of STU in order from shortest to longest if the angles of
the indicated measures. SHOW ALL WORK!
STU have
43. List the sides in order from shortest to longest.
40°
mS  x  6
mT  2x  8
C
F
mU  3x  2
X
70°
W
Y
35°
65°
Mark the picture. Complete the statement with <, >, or =.
45. m1 ______ m2
44. ON ______ LN
O
2
65°
63°
N
M
CD = 12
12
13
1
L
46. Write and solve the inequality that describes the possible values of x.
9
8
58°
(4x – 14)°
8
6
Use the figure and given information to answer #47 – 49.
B, D, and F are midpoints of ACE.
A
B
C
47. DF // __________
48. If
D
F
AE  38 , then BD  _______________
E
49. If
AC  7 x 16 and DF  5x  4 , set up an equation and solve for x. Then find AC.
x = ____________
AC = _____________
Bonus:
Three local high schools, Jefferson High, Northside High, and Smithville High, must
share a new stadium which the district is planning to build in a new sports center.
In order to be fair to the three schools, the district would like for the sports center
to be the same distance from each high school.
If you consider the three high schools to be the vertices of a triangle, what point of
concurrency would be equidistant from all three schools? What special segments of
the triangle would be used to find this point?
Jefferson
Northside
Stadium
Smithville