Geometry SOL Review Packet
LT 4:. Classifying and Ordering Triangles
Quiz Grade Section ComPlete?
-LT 5: Triangle Theorems and Segments
Quiz Grade Section Complete?
LT 6: Pythagorean Theorem
Quiz Grade Section ComPlete?
LT 7: Right Triangle TrigonometrY
Quiz Grade Section ComPlete?
LT B: Congruent Triangles
Quiz Grade Section Complete?
LT 9: Similar Triangles
Quiz Grade Section ComPlete?
PeriodName
** If found, PLEASE return me to Ms. Wilhelm, Room 2502
LT 4 - Classifying Triangles/Bigger Side, Bigger Angle
Important Concepts to KnowClassifying a Triangle
By Sides:r Scq len X-no i gdelz lsosceles
2 3 sf;/t-lEqnilqfura I
- g Ysl/es
By Angles:1' a"cuf L
r vufef t
3,
2.
3.
4.
- of tt 3 .z's ttss *hon 40'obtuse
I t- gY e c^Ft r +f,1qn 19"
ri4h*-'one L = 10'
e4i/lb^$wla r^cril3ri: (alt=t',o')A
How to Determine if it is a Triangle
rne{till4of the lengths of theSfYl4l I two sides
musr be $flqhf than the l0F$l siaes.
3,1 ','7rtnurruel rr'do:::,;l'a -ffry'::.
Bigger Side/Bigger Angle
The biggest side of a triangle is Q CYTSS from the
l" lg g tJl-angle of the triangle.
The smallest side of a triangle is ftCh(5 from the^L
,.e hA I ldllngle of the triangle.
Examples of SOL-Itike5. Which l z.
expression correctly relates the lengths ofthe sides of I
this triangle?A. AB<BC<CA|--_
I n. AB<AC.BC I
-
C. BC <AC <AB
D. AC < BC <AB
Questions
lshn wants to rnake * triangular gard*n.W*ich of the followirlg are possible diruensiotls?
by5ftby 416-|lot"tt" * I IbrB>to y'g+ tL tq.o
3. Which set of numbers represents the lengths of thesides of a triangle?
A.
B.
{26,8,1.5}{5, 18, 13}
gilf ?
ytt3tts t'?
Yt1
13 t ro=r? 1l4--r] t>{= 2j >22 t/
C L24,7D {6,17 ,22}
4. In triangle ABC, zA is obtuse. Which statement istrue about the sum of the measures of zB & zC?
tx > qo
zB vtC < 1AD. mzB + mzC = 180
A. mLB + mzC = 90
B. mzB + mzC > 90
C. mzB+mzC<9O
5.ln the trianEle shswnr {;t{ :
#ig
L2,ltk = 8, and lt(;:7,
tt
Which sratement i5 true about tfte angles in aIl{,ifi ?
F rtt.. ff is the EreateslG ntt.G is the greatest
l,{ rrr. R ls the least
J rtt '0 is the least
6.
{}n a ruap, Tannerxville, Churhvick, nrrdE;rrkersvill* ffrrm n triarrgle. Chntlrvickis ?fi ffiri1es frnm Tsnnerxville srrrlBsrkerxville is S{} xriles frillaTannelsville,'Rnrich ix * ;r*xnitrletlistcrftc* heirre*n {lhfi d$:ick nntle;"t;.,ju"ar*: R ;il ; "+'.'i.*
s\ oteJ
i i*flfi- go-lo< x< 7or1ozol x<lko
7. f,')v t4a"\ a a'w
n n *rnyhl${',/rl"}rirh xtstts.m*nt isnI'ivlrvs'truc?
m,.A * *rJ.S = tl{}":r:/A + nrJS ''::. Pff'
H ,1gl-1]g :. A{,,
,4-S + gry ',., A{,'
B.
.l-X t S q.q^0:S
{r orn;t JLhdl\asf
s1 de
Usin* ihr: inf'r'rnati,rE[r tlrc dlrru'inq.u-lii t'lr :r ttg I r' lt rr- tlr r( t'irr-t'\rc'r Ftll'u?
A /-XZY
9.
W&zi&x. &Lxt *sxuxlr6hlt,' tltr rrt eti*LbY6:B
lc'rrgtlr" ,rf tlrr.flr}'t'sitlr'c of :r gt\-r'tltz'Awz" glt?
,rf
1..*
,1 rm:1, l-3 rrn, }"fr *:t:2 {t, & &. 7:t tt
tzrzo t.rry
10.
Three lookout towers are located at points A, B, and C
on the section of a nationalforest shown in thedrawing.
Which of the following statements is true concernlng
CJ The measure of angle A is the least.
D) The measure of angle C is the least.
LT 5 - Triangle Theorems and Segments
Important Concepts to KnowAltitude
Se,gn on+ -L+g oryosl +-L
sls [t** ve(hx)
Median ,
i'4,???f'TJn,,tr wr id Poil* "fopposlte sto{ e
Angle Bisector
segmenf +ha*
ciu an aryle
in 1", a\ f
Perpendicular Bisector
se4nnenf +hal i s
A 'h) oPlaosf l-L
sr/r \ cr,,{s i* inh^\f
r"tv4,-u i5€11
Angle Sum Theorem
In symbols:
m4l +h/l rh43 3
In words:
100'
$rrn tl intertur /. su itlwtjh iS 190".
t;
In synbols:^ Ir{ *tb = cB ,-+hev\
/ k = Lg.
Isosceles Trianqf, Theorem
In words:
rf 4-stdes ar(.q A, +hen +hc
aCfuss ffrC qlJo
: tnZ5
=.
In symbols:
vtL+= w..L2+rnt3In words:
rhe %fen'ov L tseQuat J? +hl .-Su''. "fvhL z Y efio te interiurz
Exterior Angle Theorem
Examples of SOL-Like Questions2. In the diagram below, AABC is shown with AB
extended through point D.
lf mzBCD = 6x + 2, mzBAC =
3x+ 15, andmzABC=2x*1, what is the value of x?
LN+,IV= z BcD]Xr-tE t2X-t = bXFZ'
L. In AABC, An = gC. An altitude is drawn from B toAC and.intersects aC aTTlffih statement is notalways true?
c, LAW[-] z t.{WL}D rtrflA x LF.ffi'tr
A. -tF = BF
m
3. In the diagram of AABC below, AB=AC' The measure
of zB is 40". What is the measwe of zA?
C
C=t3ax: faot€o
/ +01 4o ,botX =
x:1oc) M4A:tOD
4. Find the value for x.
ff'--1;125"
5. Side PQ of APQR is extended through Q to point T.
Which statement is not alwaYs true?
A. mzRQT =mLP + mzRB. mzRQT>mzP@rD. mzRQT>mzR
Y
tn the diagram below, AC = DC = nf . tf ttremzACD = 48, find the mzB.
Findanglesl-5.
ct+ 3€Lazl=
zZ?L)=z4'tF=
32"
7. Below is a triangle. Based on the information glven,
how many sides of the triangle must be congruent?
if ) t's,7, o?T'sldt\Y
, O. 0 sides are congruent
B. 2 sides are congruent
z C. 3 sides are congruent
D. Cannot be determined fromwhat is given
rgle Drse(yz4xt I
f )1Xvl = b0 y\
J=boY,
g. Find x if mL1' = 29x * 1 and mzXVW = 60x'PV is an anqle bisector.
(rrnr)5?tXr
3x=txj
Iti. pind x if WM = 4x - L and WN = 3x. WL is a
median.1/
X
LT 6 - Pythagorean Theorem/Right Triangles
rtant Concepts to KnowPythagorean Theorem
Finding a Leg
aTrlz-C2 -bT
Finding the Hypotenuse
At.,rb^ I C
€riven 3
a'*b'a.'*bn
Applications of the Pythagorean TheoremClassifying a Triangle by Angles using Pfihagorean Theorem
srdfs of a A, a,b,L tf t
=C" -+> rigl,r+ A
> c> .-17 ACuYt- A
dzub, L C> + obfi4se A
Examples of SOL-Like estions
1, A light post, shown at the right, is set in concretu I Z. Using the triangle below, what is the length of
suzand supported with a guy wire while the concrete
dries. The length of the guy wire is 10 feet and
the ground stake is 4 feet from the bottom of the
light post. Which equation could be used to find
the height of the lightpost, x, from the ground
to the top of the lightpost?
A. x =102 -42
B. r:10? + 42
_---=-1I a, 4,17 cm \
'b. 20cm
c. z!/cmd. 7cm
"S
x)2.x =-.
t +* =(o-to'- +'
xz+ v-=8'Xz* 3to = b+
Xo = 7?)
--x: { z-alr+1
/\z7
X: ttca -rt >
4, The diagonals of a squareis the length of a side of the
8.7V3 cm
C. t4tl2 cm
D. 14J3 cm
measure 14 cm. Which
x'+ x'=fut2x,> : \4 u
x7= Ix=[ qI
L
is acute, obtuse, or
2, + ft5
3^m rni t [z . 31
6. Find the length of the base of triangle.
x'* b-= of '
'zX:' 3'{ b
6'rg>= -'l>sc, t{} =t1Y- : | 3 Base : t6:3=J-rt
5. A rope is used to pull a boat to the dock, The
rope is attached to the boat at a point 7 feetbelow the level of the pulley. What is the
distance from the boat to the dock when the rope
is25 feetout? ]"+X' = 2T-|q1 x> = b25
a. 15 ft
b. 7ft ln*-*
l*-rft---l
B. Determine if a triangle with the given sides is
acute, obtuse, or right.
@2,1,6
Right
All of the above
32- f\tto"'-
l2ao
Not enough information
a) Acute
7, Which of the following sets of lengths can
represent the measures of the sides of a righttriangle?
A 4,5,6
B 5,1_2,L5
c B,L0,t7
Az+b- = gz-
2o)4)l': )1>D 20,21.,29
K Lr 7- Right rriangle rrigonometr y K a^ftS'Important Concepts to Know
Trigonometry (SO HCAHTOA)X
.r-on4 0Y
*rrr 6,t\uvt'- K
ov1 bottol,z,'.
f th ding cth 0-P UtSe I nvers e
Xo
Sine
srh g= *Cosine
cos€ = A11
Tangent
. .n - Otanv -;l-l
Sine Inverse'tl n \
0'srn(; )
Cosine Inverse
o:cos-' (+)Tangent Inverse
O =*qn'(+)
Examoles of SOL-Like Ouestions2. Find the value of theta.
cos'(+)
Which of the following equations can be used to find
the value of x in the diagram at the right?
.80sns-- ,/A. 17H
15
A
D. All choices can be used.
3. A light post, shown at the right, is set in concrete and
supported with a guy wire while the concrete dries.
Find, to the nearest degree, the angle of elevation of
the top of the post made by the guy wire from the
stake in the ground.
c. 22"
D. 64"
cosg =+0050= +cdfr)-o otb b +
. A right triangle is shown.
easure lsl{ closest to the value of x?
oi,AtnnV -
'e yl
r-zTOnX _ftr -tlB \
X:tqn t% /xr45.l'
5. From a point, G, on the ground, the angle ofelevationof an airplane is 21e. The altitude of the plane is 2200
meters. What is the distance from point G to theairplane, to the nearest tenth of a meter?
A.2356.5metersB.3241.4metersC. 5731.2 meters
D. 61,38.9 meters.AOs\nv: E
\t - ZZ99slnd\ " )4
7:2AB
o
_,-x Ff| -'"-,..,
;*=*2-zoo
X- srn
6. Find the value of x.
l!',
Jtotqn 30 :
I0 h xta n ++ =ffi1Xt5.11t-crn4$XtL 5,5+
Y= lotqnlo'Yt 5.4?
;/r"\
7.
This ftgure m*dels a gate fhat has b*en esnctru{te* x*i*g twr paralietv@L$**rd;s w}*t a
diag*nal bsard c*nneeting thenr. Idsnfify ill* *f thc stat*m*nts that m*:xt bs trae,
sin..( ,ri r * eos" r'ir i[w1w
v':1{x;
,:intr?
)irucH9 cot lt !ft: )2
-x7
qotrJr$":$S
'131fuA-1^..-.""*-A^-oobt. rr c
/\t ^r:AsCongruent Triangles
o v'\ v- Important Concepts to KnowThe Five Postulates that Prove Congruency in Triangles
Side Side Side [ $$S )
dtl 3stdeS: \i,r b-*h
Side Angle Side ( SAS )
e s\dts qnd
1s cuvDE b dfg[eJ
:Side Angle Angle tSrA | {ffs
a onylu 1dCIfruJPoh dl*n4
hoh-'inctt{didrl?i t, :
Angle Side Angle (ASA )
2 angles crn d
tht lncludcd
s'ld e ors :
HypotenuseLeg( HL )
ln a Ri3 t'\+ A,+he hlfle,ru\cand coft'gpzond in
Le3 are t
Examples of SOL-Like QuestionsWh*t value of .x m$*es t'}"TW E arf 'I'7
er+1
3x-\
4
1.
+\-5X
A)2Bl 3r
15 which triangle relew ifno-Cpngruent to the other thlee triansles?
AA/ L:;, ' AII
g9
Affi-/' \x \'a\ rz t-, .-l
3. The diagon al AC is drawn in parallelogram ABCD.
Which method can not be used to prove thatAABC=ACDA?
IIlA. ssAl# B. SSS
C. SAS
D. ASA
EA:EW,CA=CWC
4.
).
The vertices of aAI]( and the e,prlpqlnu 41i rtuu, integral coordinetes. plot point /-with
integral coordinates so that t {BC} dl[!t)-L*Y
BL= El-
r[-8,4*....*.. -, . i
---"1
i234\A78')'
11F +'. .i
':"i--*a_*I -'-
6.
Given: ,r{ is th€ midpsint of lff and KF,K
pThe given inf*rmation is sufficient to proveaK,qt = aFPlff by whieh postulateltheor€m?
A Angle-5id*-Angle
& Siqle-5irje-Sirie
D AnSle-Angle-5id*
7.
With the inforrnation Siv*n In the drawing$'r,nhich pair of Lriangles can be proYeftcongr*-qnt gl!!s Side-Angl€-Side postulate?
JftS
u A45
5SS
B.Sel€rt ti€ res$sns lff the la* thr€c stalefirntt 0f Sk prrsf, *
*itsn:': llSlt :: i.Tr'S; {' K 7 f S
Prw*r *[,if ,:,*I&.f
Statements
J"ffi?ff
( r r,\! -r f,t\ *5&
L rfi,r nt
.,;il"lR;:I{;
l. ,,l.IJ{ l;.0rtJ
Sare anglm oi an rsnsrrlur
bi€nqk d* eongruerf
fwrspnding pa* ai e*qr*ent
t:ienqlx;rc congruerf
Rr{tu(M
g. Ciuun' ag = DE and LA=LD. Which of the following methods can be used to prove that AABC = ADEC?
anAU
B.
Side-Angle-Side
Angle-Side-Angle
Sid'e-Side-Side
D. There is insufficient information to determine in thetriangles are congruent.
/\_/
LT 9 - SimilarA^s
Triangles
l"n-lrL
Imnortant ConcePts to KnowSimilar Triangles
1. Angles: Na,hg ltJ a(e =
2. Sides:L' "'";ld es d' PnVo( fronq I
coYrrpafi 5 anRatios
of 2 gtaonfi heJ
ProPortion, b
*wo eqva\ r"1".sq c- fsttve I
?- q crussqgJ(St\ve b.l
Side Side Side Similaritv t.lSSry
\+ srdrs [o(t ))+htm b. 5 d,(c
c)ve !, +he nu s\ rnt\qr ,
Wavs to Prove Two Triangles are Similar
Angle A
1 Side Angle Side Similarity t$/ff n )
\t 3 stdes q(L VrcPo
ct^c) {Jrc tnclr'r dec] 't''S: ;..fien 5'S a(L-j
s\'rni\q r 'S\naitotrsr _ Mr
Examples of SOL-Like QuestioqqZ. t.r tit" diagram to legC and AEDC below, AE
andBD intersect at C, and zCAB=zCED'
Which method can be used to show that AABC
must be similar to AEDC?&B
30 x: T+0
4. Solve for z.
Bl =ERT 262 booz7ob :
'n8: *' 16
:- lc,+---
IE Z-\ \A
./ 2t+- LoB
3. At a certain time of the day, the shadow of a 5'
boy is B' long. The shadow of a nearby flagpole at
this same time is 28' long. How tall is the
flagpole?
-r xlrl5\c- Ll) 'ra
BX: l-l"5 fe tv
6iven: slfJi ig t*bdividerl inta cmaller ttiangle*
J? t Tana If .r. Ef ara.lT :. {-F
Point /l lies cn 17. and pcirrts ll and l. lle on i:l
8**ed ox the given infcnqation, identify two tria*g'ps that maY f{0T le *imilar'
5-Fitd th. ""tue
of x' A tS <.v
n>= 4Dx- 4ft
x=v
-he perimeter and the ratio of the lengths to the
width of a rectangle are given. Find the length and
width of the rectangle.
Perimeter: 340 ftI:w = 1'1"9
2f \lx)r-2(1x):3+ozzx{- )BX 3 3rc
4€X *- 3fo
Wtre.r tt*aing upright, Gary knows his eyes are 6 feet
above the ground level. To determine the depth of a
well, he stands in the position show. Using the given
measurements, how deeP is the well?
3b= )xK: lb?{4+
