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Smart's Mill Middle School
Geometry Semester Exam Review
2012 - 2013
You must show your work to receive credit!
Mrs. Anderson and Mrs. Cox
A note to remember, for this review AND the actual exam: It is always helpful to draw a picture.
I encourage you to do that for any problem a picture is not given. GOOD LUCK.
Name:
Date:
\3
Period: 8
Geometry Semester Exam Review
th
1
, ,
I
1. A line segment contains
J. ~~
Part 1. Fill in the blank.
G..i<'\ 0.. ~ :-\-hL
2. If AM = MB and points A, M and B are collinear, then'
O~-\p
3. In a triangle, the smallest angle is (where?)
I.
~~ 'rul..~.
\ OS ~ ",",'\c:\~~~
S~~ ~\~
%~
r-..J
4. If two parallel lines are cut by a transversal, all corresponding angles are - -­ - - 5. If A is between B and C and are collinear, then ~Pr- ~ ~c:..
~
-::.
Cd ~ Land ~
_S-=-S..=.....S=--\-\--=S~~--=S=-+l ?i.:.-..L.aSd..~~\~\ _4...:--_\l.-~--:!.......fV~s~_ C'() are methods to prove triangles congruent.
~",~"
5
The intersection of two planes is a __
-"_""'---=~-"'-=--_
6. A right triangle has (what types of angels?) \
7.
8.
s::::s \ :.
9. In quadrant
\
, the x and y coordinates are both negative.
10. Acute angles measure ~ ~
C\\:)\)
11. Equiangular triangles are also ~~~I~~-+""'=::::~~~f"U.~~~
~
12. Parallel lines have the same
13. The intersection of two lines is a
~~'\:.;
('..)
14. If two angles are supplements of congruent angles, then the two angles 05\L:=
~. ~
15. Corresponding sides of congruent triangles
16.
~
:ew lines are _~~~__'-'~~~~.l..L-and
17. The slope of a horizontal line is
(t.Qc...+c..]
.~ ~t ~~)!\\
.
r.:t
"Z...sLr'\
18. Two angles are complementary if---,-,-~",,--,-_==.:...:.
19. The angles in a triangle sum to
-=--()~~
-,­
_
_
--
and_..d.:\~~~~L...!..~~~-4~..!>d...C~~~---S~JF;!!~u..!.~~~~
21. An isosceles triangle has
a!), ~~\:J and --""""---'-~"'-'-"'~!.-l---'~"'='---":::-=---------
rv
20. Vertical angles are
.3 -=:.- \~
22. An equilateral triangle has
~
L-S
23 ;-If a-conditional statement is false, then sois its _~~~~~~~"y,.:!:,b~~
_
24. The hypotenuse of a right triangle is opposite the _--.S=D"-'-'\,"",~7~~~_'-
'
_
25. If two sides of a triangle have length 4and 6 then the third side must be
26. A(n)
'\
6
\
­
27. The slope of a vertical line is
\
D•
of a right triangle is the longest side.
•
wd>, ~I,,-X\~d..
28. In a triangle, the largest angle is ---.!~~~~L~n~_~~~~~L-":~~.j~~
29. Two lines that are not parallel or skew are
_-'--_==--='-'=-"=0-=>,-­
30. The three medians ofa triangle intersect _==-------'--'---'=---'=S...:::....;-=-:.=....:...=='---_ and
32. If two lines are parallel, then alternate interior angles are _-=I'">J=2
~===:I==:'__~
-or ~~~~~
31. When two parallel lines are cut by a transversal, the exterior angles are
Geometry Mid-Term Review 2006 - 2007
_
_
~A~--o
I Part n. Free response by chapter.!
'l'rue or false.
Chapter 1
"0.)\
~~
__
-o-~
I
D~-----=';Q
~
:G
Points A, B and H are collinear.
bL 4. Points E, J and F are collinear. \-..f",\.J.JL.
):J_hm.mu.u_ u_ H
'2". Point A lies on line m. s:.-- ~
5. Point C lines on line I. E ~
E'
J
3. Points B, C and H are coplanar.~ ~ 6. Plane ABC and plane BCF intersect at point B. t=~~~_
For questions 7 - 11, refer to the diagram at the r ~
7. Name the intersection of CD and plane P. _I<.---::U):=.:L<<-8. If TBand
_
TC were drawn, what would be their intersection? _,__
o~
--::1)-'-::::.''---==--­
9. Name the intersection ofline 1 and CD.
c
10. Name four noncoplanar points. -~=-'-t:s=>'-~-=-----'---------''--11. Write another name for plane P. ..Ji,,;l..~~'l..~''''-~ ~~
_
For questions 12, write the following using symbols. Donot draw.
12.
a. perpendicular
d. parallel
a. line segment AB ~
e. the length of line segment CD - - - ' - - ' = - - b. angle EFG L ~ G
f. the measure of angle HIJ .....:...>.....:..t...---..:e...:....:;,=-_
J-
13. Find the length of the segment with endpoints H(2, 3
h -3
+ C~-2..\
L.
1­
14. Find the midpoint of the segment:MN with endpoints M(8, 9) and N(-2, 1).
~.::1<;......\
z..
­
F
luestions 15 - 17, determine whether each statement is true of false.
1.­
~-I5. IfB is between M and T, MB = BT - MT. S; c~
16. IfC is the midpoint of AT, then CT =
! TA.~-..5\\A.9.-
17. Every segment has only one bisector.
~~
18. If
mL1~4(mL2),find mL2.
2
2Ju,b
c..,.T
~
<
L.\i.+-)( -:- \~
5x-=-\~D
)(-;.3lJ,
19. Find mLABC if BDbisects LABC,mLI = 5x-ll and mL2 = 3x+5.
For questions 20 - 23, refer to the figure at the right.
20. Name two right angles.
'L f:\QC-..e
21. Name two supplementary angles.. L
'-.--,,-~:..=:!!:
22. Name two congruent angles that are not right angles. . ~\) _L--,=~
23. Name the obtuse angle. .
L h
A~
'G
116
39
25
-=="~:;>()
0
25"
0
65
0
c
24. The measure of an angle is three times the measure of its supplement. Find the measure of the angle.
3 )(+ ~ -=- \1(0 L: ~ 0
- S~
25. Find the value of y.
A
L-\S
j -:::- \\)
26. Find mL2 if mLABC = 75 and mLI = 16. _ .....
5""""9-'-°
_
27. Find the value ofx if if mLABC =6x, mL1 = 2x+5, andmL2 =3x-1.
Geometry Mid-Term Review 2006 - 2007
S 't- -t \.1 -=- \Jd
~~l.\
2
B
1
1 JLP15
c:r-n----o.,...-,~
D
Chapter 2
For questions 1 - 3, determine if the conclusion is true or false based on the given information.
1. Given:
LARD and LCBD are adjacent angles.
Be and BA are opposite rays.
_-tp---l...\
Conjecture: LABD and ,iCBD are supplements<
;f----
2.
--
lO-c...
Given:
PQ 1- PR.
Conjecture: LRPQ is a right angle.
- =~,- - \J.JL. - =- _
A
Q,
~~
r
3. Given:
J, K and L are collinear.
Conjecture: JK + KL = JL.
For questions 4 - 6, write the statement in if-then form.
4. Two lines intersect exactly one point. f'\-==I~~~~7~:====~===~C=;~~:~?~~~E=~~
5. All tigers are cats~ Q ) ( \ "
s.
6. All right angles measure 90 egrees.
--:::L.~ ~ L
- s
..J"\~-\; '\ ~
~~
Write the converse, inverse and contraposltive of the conditionaf statement.
:3=
7. Vertical angles are
Converse~£
congruent.-::L-~,3- l-S Q.J\.).
L-S ~;;r,
~m
Inverse:~ ~ '-'5 OJ\J- ~\:)t \~ ' , \
Contrapositive:~
t~- 1\;'
~
\,)
~Db
~-,co.S) \ -\-'~ ~'?b Q...r\.Q.....
.
t>..r\L V ..II..J',~ \ crl .
"-.J
-= ­
~ (~± -=:
~ ' t \J~~ ('9 Q
j\\t>
Complete the following statements.
8. A plane contains _~~\~'\:=-_~~~~~_..,---l..L_~~~~~~~J£:~~:..L_U~..ss::~2....
9. A line contains Q,...,-\- ~ m l>\-,
~
If possible, write the conclusion. State the law of logic that you used, or write "no conclusion".
10. a) If you have a driver's license, then you may drive a car.
b) Cindy has a driver's license.
1
c)~'
f"S'o~
-
0..
11. a) If AB;:, CD, then CD;:, AB .
-
-
b)_JLCD_;:'.AB_,.Jhen CD = AB.
c) -r:
\-=­N
-
N
12. a) All right angles are congruent.
b) Vertical angles are congruent.
c)~
For questions 13 - 15, name the property of equality that justifies each statement.
13. If mLA + mLB =180 and mLA =11 0, then 11 0 + mLB =180 . 3»X?9\-Yb 2r-J t>(\
14. If AB = CD, then CD = AB. _ _
3~'\ .r'-"-~""""",,,-,,-,-.=..._------------""3'"
1
-
~
15. If mLK =-mLL then 2mLK =mLL._:-...:.....::.....:..:~~~~~~~LA2
16. In the conditional "Ifp, then q", the q is called the _~~~~~~~~
ix~
17. Find the measure of Ll .
Geometry Mid-Term Review 2006
<6
1
2007
-L~ ~O
0
~----'",,;l-~U_ _
5x-18 \01,...­
4
C6~ ~\C\""L
dl\
_
p
Chapter 3
D
}. How many pairs of skew lines does the figure at the right have? _ _~
~!)
I
~
~ ~ CfL
~FT- ~
t>l=1-
_
~O \~c.. '10
\ P\)
ex:- PB
~<:- ~
~
D
B ----=-==~
Refer to the figure below. State the transversal that forms each pair of angles. Then identify the special angle
pair name.
Y0 "
nY
2.L5andL7
~
~0~~~\XS\..>
4
I
\Y()3
A~ ~~;;~.*
5
2
B
\4b
3. L4
LI and
4.
and L8
LIO j~
~
,
?bltD bD 4D
7
~
1
5. LI and L3 ~
~~ ~
A
1~ ~
6. L4 and L9 ~
~"s"S,})q: 1~u-tJ'3V ~
yD.: IdJ
D-- ~
7. If mLI = 80, mL2 = 40, and III m, find the angle measures.
()
0
I ;'0 mLII = 6U.
mL3= \4D~mL4= L\D~mL5= \4[)~mL6=~inL7=J::ill,mL8=YDo,mL9=W ,mLIO= 40~
1
~
;.in1"t~e value ofx and y.
X=-4~
j -_ \4~
9.r----~----.::;~
~ -\-\-35 =.. \R-D
m
F"
1
ltr/
\
~ Jr '6l.\ -:.. ~D
41..l":.~)(
~ -=- U'o
\~S -::."3 x+\
the value of x so that p II q.
'J. =-10 ~
+d... -:.. \\0
~'6 ~ \()~
j =- 3to
)t
-::..4r
Y:
-5 -:. ~~
x -=- 3'5
11. .
J-- X-+-I +\ ~3 -::: \ ~\J
J..x -\-\\t\
-=-\~D
x -::.. tb
12. Tell whether a line whose slope is undefined is horizontal, vertical or neither.
-t3~---Findthe-slope ofthe line passing through ("3, -O)-and-(2, -1).
___
-I
\J ~-\=\ ~
----=J_~=--~.::::-_ _
5/ 3
~----"
14. Find the slope ofa line parallel to the line passing through (5, -3) and (8, 2).
15. Find the slope of the line perpendicular to the line passing through (4, -3) and (1, -1).
_
3/2­
"2-1-3
16. Write the equation of the line with a slope of 4 passing through (-1, 3).
17. Write the equation of the line parallel to y =
~ x +9
~--=--\
Write the equation of the line perpendicular to y
Geometry Mid-Term Review 2006 - 2007
_-"--_....=..::.>:.)(_4---'-----L­
?:J -- 4L-\) ~Io
passing through (-2, 3).
_6~_-_.i.._L-_)(_
'o~1...\
=.=!. x + 1
3
5
passing through (1, 4). --+----'~~----\
~~3+-D
'0
~
\
I
,
Chapter 4
Determine whether each statement is true or false.
1. All isosceles triangles are acute.
~~
2. An acute triangle can be equilateral. ----:l~
3. A scalene triangle is never obtuse. ~
.....
4. A right triangle can be isosceles. -:r:-l'"'\w....,.
Use the given conditions to classify each triangle by its sides a
5. llWHO,withmLW=110, WH=WO=5cm. ~b.=:...~~~~_~....J...:!~~~
6. llBAG, with mLB = 90, GB = 4 cm , BA = 3 cm.
Find the value of x.
7.
~
~-=-115x
.
~>-3X_+_56
8.
\?. 'l(-r 3k ~'-~D
~o
\'L~--\UL\
X=-~
~X -\-3\ -=- ~j(+Slv
~o
~~?S
Write a congruence statement for the congruent triangles in each diagram.
z
~
N
Q
Determine which postulate or theorem can be used to prove the triangles congruent.
Always, sometimes or never.
13. An equilateral triangle is ~ W~~S) an isosceles triangle.
14. An isosceles triangle is ~ . equilateral triangle.
15. A triangle f\ ~ has one obtuse angle and one right angle.
16. An equilateral triangle is tJ ~
an obtuse triangle.
17. An equilateral triangle is &\,\\U<l..t ~
an acute triangle.
186
Find the value ofx and y.
4y
~C)~
x
19.
,A/ y.,:o\.fl ;j=-'&1.
~
24
WJJ - ~~
21. What is the vertex for LASe?
Geometry Mid-Term Review 2006 ­ 2007
6
20.
Chapter 5
UPrGL
1. Name the triangle for which GD is a median.
'-- Name an altitude of e,.AGC.
A
f\Q:,
D
3. Name a median to AG in e,.AGC.
---
4. Name a perpendicular bisector
-ffi
PT~
to triangle
B
()---,--+---~--+--"'O
C
5. Name an angle bisector. ~ to angle ~£1~c....
List the sides of e,.WXY in order from lon5est to shortest if the angles of e,.J¥XY have the indicated measures.
6. mLW=4x-15\~mLX=7x+3q4
mLY=3x-435"
T
F
xc;:;
\ ~ )( -"2. -=-\ ~
7. mLW=5x+2l/()mLX=6x-5~b
\ 'W.X -:.. \~"'Z-
X-=- ~
mLY=48-2x ~%()
qXt--45--\~D
C\x-=
X~
'XW
X~\S
8. Two sides of a triangle are 16 and 22 centimeters in length. Determine whether 39 centimeters can be
N \J
the length of the third side?
9. Two sides ofa triangle are 21 and 24 centimeters in length. Detennine whether 40 centimeters can be
the length of the third side?
Q
Write the inequality relating eac< pair of measures.
10.
7
R
mLPRQ
mLPRS
11.
5
.1-
I
,­
A
9
_ _ mLABE
1
5
6--,-<'>---b---b
D 6
C
S
Write an inequality to describe the possible values of L
12.
~
A
X. 7 3
13.
~-8 5":""7-'~x-'6
Q
(?)
c
Geometry Mid-Term Review 2006 - 2007
P
~y'7,?
~ X - 3~3)r- 2­
7
3
\
x> Ijl,
R
XL ~D
15~
IX -\() 7.Jx+S
3x-2
10
15
~x
-5
S
L
55
G
is s
~
\35'
X
•
\~
I
Part ill: Multiple Choice
Choose the best answer for each question.
Chapter 1
C:~.?' ~d the length of the segment with endpoints L(-I, -3) and M(-6, 9).
'\ \ ~13
B. 17
C. 5
D. 12
2. Points A, B and D
A. determine a plane
,\J c. are contained in only plane P
~
® r e collinear
D. are noncoplanar points
co
B
3. What is the intersection of planes P and R.
\?
A points A, D and B
@
D. AD
C. AB
AB
R
4. What is the measure of QT ifR is between Q and T, QR = 14 and RT = 5?
A. 10
B. 11
@19
D.9
Q\\5,
C
5. Find the coor~es of the midpoint of the segment with endpoints D(6, 6) and £(-2,2).
A. (3,4) r~2, 4)
C. (4,8)
D. (1, -1)
~
6. ~at are the sides of L5?~
~WGandWF
'\)
D
,
C
7.
\
11
WB and we
~andWF
~-_. and WF
L5 and L6 are
~ adjacent
'~and
E
B
G
B. vertical
C. supplementary
B. vertical
C. supplementary
A
7
L9 are
~djacent
\?
~
D. complementary
~complementary
Ll and L2 are
B. vertical
11. Find mLl.
A. 25
C. 175
D. linear pair
C. complementary
A. adjacent
D. complementary
@inearpair
155
D.5
12. If mLABD = 40 and mLABC = 110, find mLDBC.
A. 150
B. 130
@70
D.80
C
\\D
c
Fin mLRSU if ST bisects LRSU, mLl = 4x -12 and mL2 = 2x + 6.
B
A 48
C. 9
B. 18
D. 24
Geometry Mid-Term Review 2006 - 2007
, ,
Chapter 2
the converse of "If L1 == L2, then mL1 = mL2.
~If mL1 = mL2 , then L1 == L2
B. If L1 == L2, then L2 == L1
\ \ . C. If mL1 = mL2, then mL2 = mLl.
~ D. None of these
1.
Ch~
2. IdentifY the hypothesis of the statement "If today is Tuesday, then tomorrow is Wednesday."
A. Today is not Tuesday
B. Today is Wednesday
Today is Tuesday
.
D. Tomorrow is Wednesday
Q C9
3. IdentifY the if-then form of the following: All cars have four wheels.
A. If a vehicle has four wheels, then it is a car.
If a vehicle is a car, then it has four wheels.
c. If a vehicle is not a car, then it does not have four wheels.
D. None of these
rL. ®
\ 'J
4. Choose the statement that follows (1) and (2) by the law of detachment.
(1) Right angles are congruent.
(2) LA and LB are right angles
A. mLA =90
D. mLA
B. mLE =90
=
mLB
L
5. Which statement represents the law of syllogism.
A. If P ~ q is a true conditional and p is true, then q is true.
CJ-....
If p ~ q and q ~ r are true conditionals, then p ~ r is true.
'\-)
C. If a, lYahd 'c are real numbers, then"a(b +c) = ab +- ac.
D. None ofthese
®
\1....6. The transitive
\..:..J A. b = a
prope~ equality
\!.)a = c
states "If a = band b = c, then _ _ ".
c. c = b
D. b = b
C-
~
7. LP and LQ form a linear pair and mLP 62. Find mLQ.
A. 62
B.28
@118
Geometry Mid-Term Review 2006 - 2007
D.90
9
,
I
Chapter 3
1. Given
III m
fA) 108
[A
\ \Y
18
and mL2 = 72, find mL3.
B. 72
D. 112
2. Given III m, mLl = 9x +5 and mL2 = x + 37, find the value ofx.
(L A. 32
rB~4
'6)(-:=37­
C. 41
39
X -:;:.- '-\
¥
':..J
..
A right triangle must be
A. isosceles
B. acute
C. scalene
1------;:-1'-----=m-­
111m.
D.
In AABC, what is the angle opposite AB?
A. CA
B. LA
C. LB
e­
2­
ither isosceles or scalene
~ 5x - 7 and PR = 2x + 5.
D. 4
legs of an equilateral triangle PQR ifP
C. 12
Find the measures of
A. 39
1
...
3. Given mL4=5x+2 and mL5 =3x+28,findthevalueofxsothat
A. 26
n
c. 67
D. 75
Chapter 4
3
~LC
4. In ADEF, if DE =:: DF and EF is the hypotenuse, then ADKF is
A. acute and scalene
B. right and scalene
~ right and isosceles
D. obtuse and isosceles
U
V
5. The measures of two ~es ofa triangle are 38 and 47. What is the measure of the third ~mgle?
A. 85
~95
C. 133
D. 142
().. 6. If AIGH =::AKlJ, then LH is congruent to
-~
LJ
B. Ll
.C. LX
\ CY
CJ.... 7.
V
D. LL
Which ofthe foIlowi~s not a postulate used to prove the congruence of two triangles?
A. ASA
~ SSA
C. SAS
D. SSS
8. The measure of the v~_angle of an isosceles triangle is 120. That is the measure of the base angle?
A. 60
~O
C. 35
D. 40
\::J
6 6
9. Name one additional pair of corresponding parts that need to be congruent in order to prove that
Gn;;:::::; byAS~
C. LT=::LK.
T
1}'",KO
D. ST=::MK
s
Geometry Mid··Term Review 2006 - 2007
10
K
p
M
0
Chapter 5
1. Identify the median of LlABC .
C
A
-
-
CE
B. BF
@AD
D. GH
F
2. IdentifY the altitude of LlABC .
\\.
n
~E
B BF
D. GH
C. AD
A
H
3. In LlABC, if mLABF = 39 and BF is an angle bisector, find mLBCE.
A 90
B. 51
T I C . 39
8
@12
\) 0..t.
What is the longest side of the figure QUAD.
\)
A
./
~
C@O
B
QU
U
0
·D.DA
¥10
D
;.)
5. In LlEFG, mLE= 6x - 8, mLF =7x + 3, and mL.G = 3x -7. Choose the list that shows the sides correctly
o r d e @ f r o m s h o r t e s t t o l o e s t . \ I _ \ _ _ \ ' I.. . .
~
~X~L·~
~ F:,FG,EG
B. F ,EG,GF
--f\C
--
-C. EG,GF,FE
--
-D. GF,EG,FE
\~)(-
~
.-t~
~L
\2­
tt
6. ~ermine which set of numbers can be the measures of the sides ofa triangle.
.
~13, 10, 16
B. 1,2,3
C. 5.2, 11,4.9
D. 208,9,219
wo sides ofa triangle have lengths 15 em and 19 em. Which measurement can be the length of the third side?
em
B. 4 em
A
C. 40 em
D. 36 em
e,)(+- 3"',( X.... -z..:""
8. If the sides of a triangle have measures 3x + 4, 6x - 1 and 8x + 2, find all possible values ofx.
~A x>-l
-7
3
B. X>-
D. x>O
X>-
11
5
"7
-
5...c,,-i\?
Al
\CJx+1. /~x+-\L\
@)4
J
Geometry Mid-Term Review 2006 - 2007
L
11
4)(7\2.
,!"73
"3
)(7;'\\1
9. IfM is the midpoint of JK, mL.l > mL.2, JL = lOx +- 2, and LK = 6x + 14, which is a possible value of x?
B. 2
C. 3
\
l L\ x+-\ -;. 3x+
\\'1 7
\\ y-l-Ul-' ~x- \
_
'(
Properties
State the property, theorem, postulate or definition used to make the conclusion.
--3--6~~~~~=-'-'-"--"----------
1. IfUV = VW, then VW = UV.
2. If L.Q is a right angle, then mL.Q is 90
0
•
_\~~~~~~---=~~~~_L
22~ ~
3. 2(x-50)=2x-100.
4. If L.1 and L.2areverticalangles, then
L.1~L.2. V~ ~ I.-~
-.L ~.
5. If t .l- U , then L.2 is a right angle.
6.
<~
_
B
u~
2
AB+BC=AC.
a
7. If L.1 ~ L.2, then mL.1 = mL.2.
8.
LA ~ LA.
10. T is the midpoint of SR, then ST ~ TR.
11. If L.1
~ L.2 and
L.2
~ L.3 , then L.l ~ L.3. -----'\!::::~~::..:...~.~~~~W"'~~'??~--=:::~-"'-'--------
12. If L.3 and L.4 are a linear pair, then they are supplementary.
\)~
~~~
J
C\. \.f"t.
13. If AB bisects L.eAD, then L.CAB ~ LDAB .
14. If L.4 and L.5are supplementary, then mL.4+mL.5 =180. _"'==:~~"':"--ld--!5~~¥--~-15. If 111m, then mL.l+mL.2=180.
16. L.3 ~ L.4, then
/11 m .
3
2
4
Geometry Mid-Term Review 2006 - 2007
m
..
12
R
Proofs
,,1.
Given: RFl. AT
F is a midpoint of AT
Prove: AAFR =ATFR
Ad-----6-----bT
F
E
2.
•
D
Given: EA II DC
-EB=BC
1.
1. -:lI"'t=~~-;;---,-----------------2 '-_--z=:.....::~~~I--_.L___~_ 2. _~~~~~_=.....1_....L..C~~~0f"D~...l..
_
3. ~-=....:......':,---=-~~---:::-4.
_ _--1
3. --:;~----T-7~----------------4. _----'-"-'----'----
_
•
z
3.
Prove: ZV II IT
Given: W is a midpoint of ZX
VW=WY
x
Reasons
Statements
1•
2.
3.
4.
2.'"
-="---"-o.,4-=+-=-.>.=-c......-:.;i:'"'-_ _:.....A_
1. --A-~-.::.....~---,..____----;:-----------2. ---"-"""""''Pr-::.p....=.F-~~~\=d,9''-''''''': ,\..".lO-,-~=--
_
3. ~....::.=...-'---=-_--L..-S=----~~~-==-=rn""'\--'---''--------.
4. _--=-\,-~w.:-:
.
_
5,
5. _ _~~..l--
6.
6.
7.
7
----'=~~
_
.
_
--"'="O~::......:."'_'_______=::.......L_~"_"__'_=~"""=....._.._---------
Geometry Mid-Term Review 2006 ­ 2007
13
Given: 3(2x - 5) + 1 = 2(x - 3)
4.
Prove: x= 2
Statements
Reasons
1._---iT-.------;-----:-_--.----
_
2._.",........-==-=-='---'-+-=....:;;;;::.=:
_
3.---:~~~~~~!.....l.----­
4._....".u~<p',~1.."..Jo.~"-L-----­
5._-:::--'-..=..::.:=-..:"-"'-':""""""-'-
_
6._..........--'--.%-.-"-.=....:::.=..:.~
_
d
Given: a II b
LI ==L4
5.
Prove:
ell
a
2
d
_ - - - - - - - - - - t --------.+-~
3
Statements
-­
L
a-I-I-b­
2. LI ==
3. L3 ==
4. LI ==
5. L3 ==
6.
Reasons
ell
L3
Ll
L4
L4
d
Geometry Mid-Term Review 2006 - 2007
14