Download Median G C

Per--
Geometry
N[\,? Unit 3
Unit 3 Practice Assessment
Content trou are
S..e
Know the following terrrs: Angle bisector, median, altitude,
perpendicular bisector, exterior ang1e, remote interior angles, linear pair,
supplementary angles, complementary angles, r'ertical angles, rnidpoint,
alternate interior angles, alternate exterior angles, same-srcle lntenor
angles, corresponding angles
Three angles ofa triangle add to r8o degrees.
Alinear pair is supplementary.
Four angles ofa quadrilateral add to 36o degrees.
An angle bisebtor divides an angle into z congment angles.
A midpoint divides a segment into z congruent segments.
Parallel lines and a transversal create angle pairs that are either congruent
or supplementary.
The measure of an exterior angle of a iriangle is equal to the sum of the z
remote interior angles.
e.Ii..ts
Use the properties of all parallelograms (including rectangle, rhombus,
square) to find measures of segments or angles within a parallelogram or
rtrite an equation that can be solved to find a missing measure.
Be able to justifii the equation you've ntitten.
Determine u'hether a quadrilateral with given features can be prot'en to be a
parallelogram, rectangle, rhombus, or square.
IJse the diagrarn to name each angle pair.
Sunplementarv or Congruent?
Angle Pair name
Ansle pairs
19 & 114
t/crl>.1 o ro(nr
lrtuorhL.-*
-r
r.
/.6 & l8
/.1 & ltz
L5 &, L9
13 &, 116
2.2 & z.r4
lls & lt6
16 & ztz
/, o
a.
rres
Doh
),'^/
a na/i.-g
/1, l^- (oJr\hr'r,'rr
,fon-.r,t L
r)-lo r^iaf
nlkr;-la-fi*a e -
Lln-r.
n F?r-r'
,f t- zt/{,*o-/nrt
et*er,'ot'
rrLle ! r
/a-ir
-
{o
t
t'o
*o rr o ^-*
lk4nrt,. ^&
f
/"f,4ort ta{
z. Identifiz the segment/1ine that fits each term from the sketch.
Median
Altitude
GC
1
C4
tb
Angle Bisector UA
PerpendicularBisector
bg
'/
rr. .Ln[.,, ^ /- -u
r:I!-n{, -,.'L,n^/
s {n/a/)'nn^ lal,t
Write an equation to find the value of x. Then findthe measnres of the z angles.
tnlt='71
z,/ = lx
)(=F
lr1/-> = 1lt
: i:sx + l1}", arI.4 : {l*:r
2 1 t+ tl + /,( *+tl . /f,l
4. ml3
)(='f
.o
?1 tf trt =ltr,
lhL ? ? /o I
m L{ .- 770
11*. = /,t/
5. nlld
:
i'37-r,
-
15)", r'rrr5
=
/7t-t{ = lrtt-r?
/'f a 7*
t(=L
hL1 = /?to
n/(,
2.11
6. rldt
:
L
{fi.r +
I4)",
ml,l : il;x
w z{ = /7{-1
!1-
/l
r
{.*J
fUt,P
Ct7.
{4,J-r
-q
t l/>_
/= 7
0
lhtl= Jo
filtz ld"
Find the value of each variable shown and provide a justification for each equation or
calculation.
7. Find the
measure of angle CAB.
tO,r
-
B. Find x. Then find the measures
of all marked angles.
9. Find x, y, and z if the figure
shovtryr
{15x
lt]
ly+
t5x
{&x
+ bl
tLn
{tlx +
It
/o{.-/t +lt = lay-{
/oLt-2a?/.*-{
L{,
+
>L
L= /L
th- L lAd = t{,r)'1
}7}*
// ( * /7-
?}"i
7
+ 'ifr}'
/{t
f
is a parallelogram.
t-
t"
6y-15
gz
=
r{
"7*'?'
2L=
-/f
d
?a
r (t) *t= ,/ c"
tc /t) =*_ ?o
0
{18x +.44}-
?- /ox +{f
Ztl-= /L
L(L) 5lu
tr (() +l>,
+:
?z + :. = L't.f
1Z = 2{.(
rc.
Complete the proof by providing tlic missing statements or justifications.
Proof statement
Diasram and infonnation
It is givcn rhat IQJiS lx a pa;allels:grfrrfl."Ih* diag*nals *f a
. E1: LIr*
paralSel*grar,u bisect each othi:r, so Ff = &,.
&rflexire trr*perq: af Ctngruence, Q7= ts.
" It is giv*n
'7
d.
{;i','rrr: FQfi-qis apara.trtreJfrgr'frr}}.
f'{\:ivti FfJtrS is a rhcetbns.
ffif F
Fill in the missing information from the proof
a.
{2
e. s Ar
tirat ffi i 85. sc ISTF arld ,/QfE arc r:i1"I'it angi*s h1, ih*
drfrnition o,f r r,.4 . Then lQlF = d{ii Ii by tle* d. { .
S*&S7?=&QIFL'r1'e. ? .andQr=f. ? ,trrytlFCTC.
St fh**r*m S-5-3, if anr pair r:f c*ns*rctit'* sid*s *f a
'
paraihlagranr &:1:i coDgrT-iEnt, then rhe parallel*g"rarn is a
g" ? . Thercfiilru FqeS is rltr:rnbree
statement above:
b. nr
,. il.
d.
AY- rr/ra-rP
r ltu*lq,
e.
rif l? eyLr
rr.
Complete the table. Place a check mark under the name of each figure for rvhich the property is always true.
1.
The diagonals areperpendicular
fhe figure has four right angles
'[he opposite sides are congruent
Parallelogram
2.
3.
4. The diagonals are congruent
5. The figure has four congruent sides
6. The diagonals bisect eachother
7. The consecutive angles are supplementary
8. Each diagonal bisects a pair ofopposite angies
9. The figure has exactly four lines of symmetry
10. Tlie figure is a rectangle
rz.
Rhombus
Rectangle
Square
t-
t/
t/
t/
t/
ta
t-
t-
t/
t-
t/
U./
tL/
l-
l/'
t/'
t-
t/
,/
t/
t/
Given lines m and n are parallel and o and p are parallel, find the values of the requested variables:
b=
b
/o
*= b0o
a= (a-
,=
{a
informations make the quadrilateral a PARALLELCGRAM? If the information does not
guarantee a parallelogram, sketch a counterexample that deomonstrates another possible shape having
13. Does the given
the same characteristlcs.
fi
&*i.ll
E
1
1)
ftis
alu'e3-i fcrrrn a pruailclogr*ioT
S]
lf
i
rhi.s sle'al"s
form i: paraflelogram?
YtS y'\
XruO $rerir{*x r.rletderc**r;rle}
ltill ihis.al*'ays famt * parallelogra;'rt?
+o*at*rcrraph}
n Yes
KF{* trm*c*
IfiJ WrII t&is,atrr+xSu forsa
Riil. this alrx'ays f+m ap*ra3}e}+grsmT
(prorride s 6ss,rt*r+ss, ple)
n Yec
I3)
$*-
AJo
g
r No {pr*ti*eac*urkr*r*mpde}
$ this aI:anys form * p*rd1*,1*Sretr?
fF
(T
Wili this airvays foru. a prr.rilclo1saml'
u Y*s V Hu ftrrevid* n wuutems*mplr)
I
!V**
y'\
[f
lelsgr*:E?
Sil'el: #,Li{-$
is x
p;*t*}1*.}F.erwry-!
Frt]t'*: &gJ3,{ c,L4il'$
f]
a&b4
J
AAilQ b?,4,r4