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TRANSCRIPT
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
2
Janu
ary
2013
Acu
te A
ngle
A
n an
gle
that
mea
sure
s gr
eate
r tha
n 0°
but
less
than
90°
. An
angl
e la
rger
than
a z
ero
angl
e bu
t sm
alle
r th
an a
righ
t ang
le.
Acu
te T
riang
le
A tr
iang
le in
whi
ch e
ach
angl
e m
easu
res
less
than
90°
(i.e
., th
ere
are
thre
e ac
ute
angl
es).
Alti
tude
(of a
Sol
id)
The
shor
test
line
seg
men
t bet
wee
n th
e ba
se a
nd th
e op
posi
te v
erte
x of
a p
yram
id o
r con
e, w
ith o
ne
endp
oint
at t
he v
erte
x. T
he s
horte
st li
ne s
egm
ent b
etw
een
two
base
s of
a p
rism
or c
ylin
der.
The
line
segm
ent i
s pe
rpen
dicu
lar t
o th
e ba
se(s
) of t
he s
olid
. The
alti
tude
may
ext
end
from
eith
er th
e ba
se o
f the
so
lid o
r fro
m th
e pl
ane
exte
ndin
g th
roug
h th
e ba
se. I
n a
right
sol
id, t
he a
ltitu
de c
an b
e fo
rmed
at t
he
cent
er o
f the
bas
e(s)
.
Alti
tude
(of a
Tria
ngle
) A
line
seg
men
t with
one
end
poin
t at a
ver
tex
of th
e tri
angl
e th
at is
per
pend
icul
ar to
the
side
opp
osite
the
verte
x. T
he o
ther
end
poin
t of t
he a
ltitu
de m
ay e
ither
be
on th
e si
de o
f the
tria
ngle
or o
n th
e lin
e ex
tend
ing
thro
ugh
the
side
.
Ana
lytic
Geo
met
ry
The
stud
y of
geo
met
ry u
sing
alg
ebra
(i.e
., po
ints
, lin
es, a
nd s
hape
s ar
e de
scrib
ed in
term
s of
thei
r co
ordi
nate
s, th
en a
lgeb
ra is
use
d to
pro
ve th
ings
abo
ut th
ese
poin
ts, l
ines
, and
sha
pes)
. The
des
crip
tion
of g
eom
etric
figu
res
and
thei
r rel
atio
nshi
ps w
ith a
lgeb
raic
equ
atio
ns o
r vic
e-ve
rsa.
Ang
le
The
incl
inat
ion
betw
een
inte
rsec
ting
lines
, lin
e se
gmen
ts, a
nd/o
r ray
s m
easu
red
in d
egre
es (e
.g.,
a 90
° in
clin
atio
n is
a ri
ght a
ngle
). Th
e fig
ure
is o
ften
repr
esen
ted
by tw
o ra
ys th
at h
ave
a co
mm
on e
ndpo
int.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
3
Janu
ary
2013
Ang
le B
isec
tor
A li
ne, l
ine
segm
ent,
or ra
y w
hich
cut
s a
give
n an
gle
in h
alf c
reat
ing
two
cong
ruen
t ang
les.
Exa
mpl
e:
Arc
(of a
Circ
le)
Any
con
tinuo
us p
art o
f a c
ircle
bet
wee
n tw
o po
ints
on
the
circ
le.
Are
a Th
e m
easu
re, i
n sq
uare
uni
ts o
r uni
ts2 , o
f the
sur
face
of a
pla
ne fi
gure
(i.e
., th
e nu
mbe
r of s
quar
e un
its it
ta
kes
to c
over
the
figur
e).
Bas
e (T
hree
Dim
ensi
ons)
In
a c
one
or p
yram
id, t
he fa
ce o
f the
figu
re w
hich
is o
ppos
ite th
e ve
rtex.
In a
cyl
inde
r or p
rism
, eith
er o
f th
e tw
o fa
ces
of th
e fig
ure
whi
ch a
re p
aral
lel a
nd c
ongr
uent
.
Bas
e (T
wo
Dim
ensi
ons)
In
an
isos
cele
s tri
angl
e, th
e si
de o
f the
figu
re w
hich
is a
djac
ent t
o th
e co
ngru
ent a
ngle
s. In
a tr
apez
oid,
ei
ther
of t
he p
aral
lel s
ides
of t
he fi
gure
.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
4
Janu
ary
2013
Cen
tral
Ang
le (o
f a C
ircle
) A
n an
gle
who
se v
erte
x is
at t
he c
ente
r of a
circ
le a
nd w
hose
sid
es a
re ra
dii o
f tha
t circ
le. E
xam
ple:
∠
PO
Q w
ith v
erte
x O
Cen
tral
Ang
le (o
f a
Reg
ular
Pol
ygon
) A
n an
gle
who
se v
erte
x is
at t
he c
ente
r of t
he p
olyg
on a
nd w
hose
sid
es in
ters
ect t
he re
gula
r pol
ygon
at
adja
cent
ver
tices
.
Cen
troi
d A
poi
nt o
f con
curre
ncy
for a
tria
ngle
that
can
be
foun
d at
the
inte
rsec
tion
of th
e th
ree
med
ians
of t
he
trian
gle.
Thi
s po
int i
s al
so th
e ce
nter
of b
alan
ce o
f a tr
iang
le w
ith u
nifo
rm m
ass.
It is
som
etim
es re
ferre
d to
as
the
“cen
ter o
f gra
vity
.” E
xam
ple:
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
5
Janu
ary
2013
Cho
rd
A li
ne s
egm
ent w
hose
two
endp
oint
s ar
e on
the
perim
eter
of a
circ
le. A
par
ticul
ar ty
pe o
f cho
rd th
at
pass
es th
roug
h th
e ce
nter
of t
he c
ircle
is c
alle
d a
diam
eter
. A c
hord
is p
art o
f a s
ecan
t of t
he c
ircle
. E
xam
ple:
Circ
le
A tw
o-di
men
sion
al fi
gure
for w
hich
all
poin
ts a
re th
e sa
me
dist
ance
from
its
cent
er. I
nfor
mal
ly, a
per
fect
ly
roun
d sh
ape.
The
circ
le is
nam
ed fo
r its
cen
ter p
oint
. Exa
mpl
e:
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
6
Janu
ary
2013
Circ
umce
nter
A
poi
nt o
f con
curre
ncy
for a
tria
ngle
that
can
be
foun
d at
the
inte
rsec
tion
of th
e th
ree
perp
endi
cula
r bi
sect
ors
of th
e tri
angl
e. T
his
poin
t is
also
the
cent
er o
f a c
ircle
that
can
be
circ
umsc
ribed
abo
ut th
e tri
angl
e. E
xam
ple:
Circ
umfe
renc
e (o
f a
Circ
le)
The
tota
l mea
sure
d di
stan
ce a
roun
d th
e ou
tsid
e of
a c
ircle
. The
circ
le’s
per
imet
er. M
ore
form
ally
, a
com
plet
e ci
rcul
ar a
rc.
Circ
umsc
ribed
Circ
le
A c
ircle
aro
und
a po
lygo
n su
ch th
at e
ach
verte
x of
the
poly
gon
is a
poi
nt o
n th
e ci
rcle
.
Col
inea
r Tw
o or
mor
e po
ints
that
lie
on th
e sa
me
line.
Com
posi
te (C
ompo
und)
Fi
gure
(Sha
pe)
A fi
gure
mad
e fro
m tw
o or
mor
e ge
omet
ric fi
gure
s (i.
e., f
rom
“sim
pler
” fig
ures
).
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
7
Janu
ary
2013
Con
e A
thre
e-di
men
sion
al fi
gure
with
a s
ingl
e ci
rcul
ar b
ase
and
one
verte
x. A
cur
ved
surfa
ce c
onne
cts
the
base
and
the
verte
x. T
he s
horte
st d
ista
nce
from
the
base
to th
e ve
rtex
is c
alle
d th
e al
titud
e. If
the
altit
ude
goes
thro
ugh
the
cent
er o
f the
bas
e, th
e co
ne is
cal
led
a “ri
ght c
one”
; oth
erw
ise,
it is
cal
led
an
“obl
ique
con
e.” U
nles
s ot
herw
ise
spec
ified
, it m
ay b
e as
sum
ed a
ll co
nes
are
right
con
es. E
xam
ple:
co
ne
Con
grue
nt F
igur
es
Two
or m
ore
figur
es h
avin
g th
e sa
me
shap
e an
d si
ze (i
.e.,
mea
sure
). A
ngle
s ar
e co
ngru
ent i
f the
y ha
ve
the
sam
e m
easu
re. L
ine
segm
ents
are
con
grue
nt if
they
hav
e th
e sa
me
leng
th. T
wo
or m
ore
shap
es o
r so
lids
are
said
to b
e co
ngru
ent i
f the
y ar
e “id
entic
al” i
n ev
ery
way
exc
ept f
or p
ossi
bly
thei
r pos
ition
. W
hen
cong
ruen
t fig
ures
are
nam
ed, t
heir
corre
spon
ding
ver
tices
are
list
ed in
the
sam
e or
der (
e.g.
, if
trian
gle
AB
C is
con
grue
nt to
tria
ngle
XYZ
, the
n ve
rtex
C c
orre
spon
ds to
ver
tex
Z).
Con
vers
ion
The
proc
ess
of c
hang
ing
the
form
of a
mea
sure
men
t, bu
t not
its
valu
e (e
.g.,
4 in
ches
con
verts
to 1 3
foot
;
4 sq
uare
met
ers
conv
erts
to 0
.000
004
squa
re k
ilom
eter
s; 4
cub
ic fe
et c
onve
rts to
6,9
12 c
ubic
inch
es).
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
8
Janu
ary
2013
Coo
rdin
ate
Plan
e A
pla
ne fo
rmed
by
perp
endi
cula
r num
ber l
ines
. The
hor
izon
tal n
umbe
r lin
e is
the
x-ax
is, a
nd th
e ve
rtica
l nu
mbe
r lin
e is
the
y-ax
is. T
he p
oint
whe
re th
e ax
es m
eet i
s ca
lled
the
orig
in. E
xam
ple:
co
ordi
nate
pla
ne
Coo
rdin
ates
Th
e or
dere
d pa
ir of
num
bers
giv
ing
the
loca
tion
or p
ositi
on o
f a p
oint
on
a co
ordi
nate
pla
ne. T
he o
rder
ed
pairs
are
writ
ten
in p
aren
thes
es (e
.g.,
(x, y
) whe
re th
e x-
coor
dina
te is
the
first
num
ber i
n an
ord
ered
pai
r an
d re
pres
ents
the
horiz
onta
l pos
ition
of a
n ob
ject
in a
coo
rdin
ate
plan
e an
d th
e y-
coor
dina
te is
the
seco
nd n
umbe
r in
an o
rder
ed p
air a
nd re
pres
ents
the
verti
cal p
ositi
on o
f an
obje
ct in
a c
oord
inat
e pl
ane)
.
Cop
lana
r Tw
o or
mor
e fig
ures
that
lie
in th
e sa
me
plan
e.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
9
Janu
ary
2013
Cor
resp
ondi
ng A
ngle
s P
airs
of a
ngle
s ha
ving
the
sam
e re
lativ
e po
sitio
n in
geo
met
ric fi
gure
s (i.
e., a
ngle
s on
the
sam
e si
de o
f a
trans
vers
al fo
rmed
whe
n tw
o pa
ralle
l lin
es a
re in
ters
ecte
d by
the
trans
vers
al; f
our s
uch
pairs
are
form
ed,
and
the
angl
es w
ithin
the
pairs
are
equ
al to
eac
h ot
her).
Cor
resp
ondi
ng a
ngle
s ar
e eq
ual i
n m
easu
re.
Cor
resp
ondi
ng P
arts
Tw
o pa
rts (a
ngle
s, s
ides
, or v
ertic
es) h
avin
g th
e sa
me
rela
tive
posi
tion
in c
ongr
uent
or s
imila
r fig
ures
. W
hen
cong
ruen
t or s
imila
r fig
ures
are
nam
ed, t
heir
corre
spon
ding
ver
tices
are
list
ed in
the
sam
e or
der
(e.g
., if
trian
gle
AB
C is
sim
ilar t
o tri
angl
e XY
Z, th
en v
erte
x C
cor
resp
onds
to v
erte
x Z)
. See
als
o co
rresp
ondi
ng a
ngle
s an
d co
rresp
ondi
ng s
ides
.
Cor
resp
ondi
ng S
ides
Tw
o si
des
havi
ng th
e sa
me
rela
tive
posi
tion
in tw
o di
ffere
nt fi
gure
s. If
the
figur
es a
re c
ongr
uent
or
sim
ilar,
the
side
s m
ay b
e, re
spec
tivel
y, e
qual
in le
ngth
or p
ropo
rtion
al.
Cos
ine
(of a
n An
gle)
A
trig
onom
etric
ratio
with
in a
righ
t tria
ngle
. The
ratio
is th
e le
ngth
of t
he le
g ad
jace
nt to
the
angl
e to
the
leng
th o
f the
hyp
oten
use
of th
e tri
angl
e.
cosi
ne o
f an
angl
e =
leng
th o
f adj
acen
t leg
leng
th o
f hyp
oten
use
Cub
e A
thre
e-di
men
sion
al fi
gure
(e.g
., a
rect
angu
lar s
olid
or p
rism
) hav
ing
six
cong
ruen
t squ
are
face
s.
Exa
mpl
e:
cu
be
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
10
Ja
nuar
y 20
13
Cyl
inde
r A
thre
e-di
men
sion
al fi
gure
with
two
circ
ular
bas
es th
at a
re p
aral
lel a
nd c
ongr
uent
and
join
ed b
y st
raig
ht
lines
cre
atin
g a
late
ral s
urfa
ce th
at is
cur
ved.
The
dis
tanc
e be
twee
n th
e ba
ses
is c
alle
d an
alti
tude
. If t
he
altit
ude
goes
thro
ugh
the
cent
er o
f the
bas
es, t
he c
ylin
der i
s ca
lled
a “ri
ght c
ylin
der”;
oth
erw
ise,
it is
ca
lled
an “o
bliq
ue c
ylin
der.”
Unl
ess
othe
rwis
e sp
ecifi
ed, i
t may
be
assu
med
all
cylin
ders
are
righ
t cy
linde
rs. E
xam
ple:
cy
linde
r
Deg
ree
A u
nit o
f ang
le m
easu
re e
qual
to
1 360
of a
com
plet
e re
volu
tion.
The
re a
re 3
60 d
egre
es in
a c
ircle
. The
sym
bol f
or d
egre
e is
° (e
.g.,
45°
is re
ad “4
5 de
gree
s”).
Dia
gona
l A
ny li
ne s
egm
ent,
othe
r tha
n a
side
or e
dge,
with
in a
pol
ygon
or p
olyh
edro
n th
at c
onne
cts
one
verte
x w
ith a
noth
er v
erte
x.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
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ary
Jan
uar
y 2
01
3
Pe
nnsy
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ia D
epar
tmen
t of E
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Page
11
Ja
nuar
y 20
13
Dia
met
er (o
f a C
ircle
) A
line
seg
men
t tha
t has
end
poin
ts o
n a
circ
le a
nd p
asse
s th
roug
h th
e ce
nter
of t
he c
ircle
. It i
s th
e lo
nges
t ch
ord
in a
circ
le. I
t div
ides
the
circ
le in
hal
f. Ex
ampl
e:
di
amet
er
Dire
ct P
roof
Th
e tru
th o
r val
idity
of a
giv
en s
tate
men
t sho
wn
by a
stra
ight
forw
ard
com
bina
tion
of e
stab
lishe
d fa
cts
(e.g
., ex
istin
g ax
iom
s, d
efin
ition
s, th
eore
ms)
, with
out m
akin
g an
y fu
rther
ass
umpt
ions
(i.e
., a
sequ
ence
of
sta
tem
ents
sho
win
g th
at if
one
thin
g is
true
, the
n so
met
hing
follo
win
g fro
m it
is a
lso
true)
.
Dis
tanc
e be
twee
n Tw
o Po
ints
Th
e sp
ace
show
ing
how
far a
part
two
poin
ts a
re (i
.e.,
the
shor
test
leng
th b
etw
een
them
).
Edge
Th
e lin
e se
gmen
t whe
re tw
o fa
ces
of a
pol
yhed
ron
mee
t (e.
g., a
rect
angu
lar p
rism
has
12
edge
s). T
he
endp
oint
s of
an
edge
are
ver
tices
of t
he p
olyh
edro
n.
Endp
oint
A
poi
nt th
at m
arks
the
begi
nnin
g or
the
end
of a
line
seg
men
t; a
poin
t tha
t mar
ks th
e be
ginn
ing
of a
ray.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
12
Ja
nuar
y 20
13
Equi
late
ral T
riang
le
A tr
iang
le w
here
all
side
s ar
e th
e sa
me
leng
th (i
.e.,
the
side
s ar
e co
ngru
ent).
Eac
h of
the
angl
es in
an
equi
late
ral t
riang
le is
60°
. Thu
s, th
e tri
angl
e is
als
o “e
quia
ngul
ar.”
Exam
ple:
eq
uila
tera
l tria
ngle
ABC
Exte
rior A
ngle
A
n an
gle
form
ed b
y a
side
of a
pol
ygon
and
an
exte
nsio
n of
an
adja
cent
sid
e. T
he m
easu
re o
f the
ex
terio
r ang
le is
sup
plem
enta
ry to
the
mea
sure
of t
he in
terio
r ang
le a
t tha
t ver
tex.
Face
A
pla
ne fi
gure
or f
lat s
urfa
ce th
at m
akes
up
one
side
of a
thre
e-di
men
sion
al fi
gure
or s
olid
figu
re. T
wo
face
s m
eet a
t an
edge
, thr
ee o
r mor
e fa
ces
mee
t at a
ver
tex
(e.g
., a
cube
has
6 fa
ces)
. See
als
o la
tera
l fa
ce.
Figu
re
Any
com
bina
tion
of p
oint
s, li
nes,
rays
, lin
e se
gmen
ts, a
ngle
s, p
lane
s, o
r cur
ves
in tw
o or
thre
e di
men
sion
s. F
orm
ally
, it i
s an
y se
t of p
oint
s on
a p
lane
or i
n sp
ace.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
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ligi
ble
Con
ten
t G
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ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
13
Ja
nuar
y 20
13
Hyp
oten
use
The
long
est s
ide
of a
righ
t tria
ngle
(i.e
., th
e si
de a
lway
s op
posi
te th
e rig
ht a
ngle
). E
xam
ple:
rig
ht tr
iang
le A
BC
, with
hyp
oten
use
AC
Ince
nter
A
poi
nt o
f con
curre
ncy
for a
tria
ngle
that
can
be
foun
d at
the
inte
rsec
tion
of th
e th
ree
angl
e bi
sect
ors
of
the
trian
gle.
Thi
s po
int i
s al
so th
e ce
nter
of a
circ
le th
at c
an b
e in
scrib
ed w
ithin
the
trian
gle.
Exa
mpl
e:
Indi
rect
Pro
of
A s
et o
f sta
tem
ents
in w
hich
a fa
lse
assu
mpt
ion
is m
ade.
Usi
ng tr
ue o
r val
id a
rgum
ents
, a s
tate
men
t is
arriv
ed a
t, bu
t it i
s cl
early
wro
ng, s
o th
e or
igin
al a
ssum
ptio
n m
ust h
ave
been
wro
ng. S
ee a
lso
proo
f by
cont
radi
ctio
n.
Insc
ribed
Circ
le
A c
ircle
with
in a
pol
ygon
suc
h th
at e
ach
side
of t
he p
olyg
on is
tang
ent t
o th
e ci
rcle
.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
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ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
14
Ja
nuar
y 20
13
Inte
rior A
ngle
A
n an
gle
form
ed b
y tw
o ad
jace
nt s
ides
of a
pol
ygon
. The
com
mon
end
poin
t of t
he s
ides
form
the
verte
x of
the
angl
e, w
ith th
e in
clin
atio
n of
mea
sure
bei
ng o
n th
e in
side
of t
he p
olyg
on.
Inte
rsec
ting
Line
s Tw
o lin
es th
at c
ross
or m
eet e
ach
othe
r. Th
ey a
re c
opla
nar,
have
onl
y on
e po
int i
n co
mm
on, h
ave
slop
es th
at a
re n
ot e
qual
, are
not
par
alle
l, an
d fo
rm a
ngle
s at
the
poin
t of i
nter
sect
ion.
Irreg
ular
Fig
ure
A fi
gure
that
is n
ot re
gula
r; no
t all
side
s an
d/or
ang
les
are
cong
ruen
t.
Isos
cele
s Tr
iang
le
A tr
iang
le th
at h
as a
t lea
st tw
o co
ngru
ent s
ides
. The
third
sid
e is
cal
led
the
base
. The
ang
les
oppo
site
th
e eq
ual s
ides
are
als
o co
ngru
ent.
Exa
mpl
e:
is
osce
les
trian
gle
ABC
, with
bas
e B
C
Late
ral F
ace
Any
face
or s
urfa
ce o
f a th
ree-
dim
ensi
onal
figu
re o
r sol
id th
at is
not
a b
ase.
K
eyst
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Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
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ary
Jan
uar
y 2
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3
Pe
nnsy
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ia D
epar
tmen
t of E
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tion
Page
15
Ja
nuar
y 20
13
Leg
(of a
Rig
ht T
riang
le)
Eith
er o
f the
two
side
s th
at fo
rm a
righ
t ang
le in
a ri
ght t
riang
le. I
t is
one
of th
e tw
o sh
orte
r sid
es o
f the
tri
angl
e an
d al
way
s op
posi
te a
n ac
ute
angl
e. It
is n
ot th
e hy
pote
nuse
. Exa
mpl
e:
rig
ht tr
iang
le A
BC
, with
legs
AB
and
BC
Line
A
figu
re w
ith o
nly
one
dim
ensi
on—
leng
th (n
o w
idth
or h
eigh
t). A
stra
ight
pat
h ex
tend
ing
in b
oth
dire
ctio
ns w
ith n
o en
dpoi
nts.
It is
con
side
red
“nev
er e
ndin
g.” F
orm
ally
, it i
s an
infin
ite s
et o
f con
nect
ed
poin
ts (i
.e.,
a se
t of p
oint
s so
clo
sely
set
dow
n th
ere
are
no g
aps
or s
pace
s be
twee
n th
em).
The
line
AB
is w
ritte
n , w
here
A a
nd B
are
two
poin
ts th
roug
h w
hich
the
line
pass
es. E
xam
ple:
lin
e A
B (
)
Line
Seg
men
t A
par
t or p
iece
of a
line
or r
ay w
ith tw
o fix
ed e
ndpo
ints
. For
mal
ly, i
t is
the
two
endp
oint
s an
d al
l poi
nts
betw
een
them
. The
line
seg
men
t AB
is w
ritte
n A
B, w
here
A a
nd B
are
the
endp
oint
s of
the
line
segm
ent.
Exa
mpl
e:
lin
e se
gmen
t AB
(A
B)
K
eyst
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Exam
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eom
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essm
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chor
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Page
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Ja
nuar
y 20
13
Line
ar M
easu
rem
ent
A m
easu
rem
ent t
aken
in a
stra
ight
line
.
Logi
c St
atem
ent
(Pro
posi
tion)
A
sta
tem
ent e
xam
ined
for i
ts tr
uthf
ulne
ss (i
.e.,
prov
ed tr
ue o
r fal
se).
Med
ian
(of a
Tria
ngle
) A
line
seg
men
t with
one
end
poin
t at t
he v
erte
x of
a tr
iang
le a
nd th
e ot
her e
ndpo
int a
t the
mid
poin
t of t
he
side
opp
osite
the
verte
x.
Mid
poin
t Th
e po
int h
alf-w
ay b
etw
een
two
give
n po
ints
(i.e
., it
divi
des
or s
plits
a li
ne s
egm
ent i
nto
two
cong
ruen
t lin
e se
gmen
ts).
Obt
use
Ang
le
An
angl
e th
at m
easu
res
mor
e th
an 9
0° b
ut le
ss th
an 1
80°.
An
angl
e la
rger
than
a ri
ght a
ngle
but
sm
alle
r th
an a
stra
ight
ang
le.
Obt
use
Tria
ngle
A
tria
ngle
with
one
ang
le th
at m
easu
res
mor
e th
an 9
0° (i
.e.,
it ha
s on
e ob
tuse
ang
le a
nd tw
o ac
ute
angl
es).
Ord
ered
Pai
r A
pai
r of n
umbe
rs, (
x, y
), w
ritte
n in
a p
artic
ular
ord
er th
at in
dica
tes
the
posi
tion
of a
poi
nt o
n a
coor
dina
te
plan
e. T
he fi
rst n
umbe
r, x,
repr
esen
ts th
e x-
coor
dina
te a
nd is
the
num
ber o
f uni
ts le
ft or
righ
t fro
m th
e or
igin
; the
sec
ond
num
ber,
y, re
pres
ents
the
y-co
ordi
nate
and
is th
e nu
mbe
r of u
nits
up
or d
own
from
the
orig
in.
Orig
in
The
poin
t (0,
0) o
n a
coor
dina
te p
lane
. It i
s th
e po
int o
f int
erse
ctio
n fo
r the
x-a
xis
and
the
y-ax
is.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
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ligi
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ten
t G
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ary
Jan
uar
y 2
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Pe
nnsy
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ia D
epar
tmen
t of E
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tion
Page
17
Ja
nuar
y 20
13
Ort
hoce
nter
A
poi
nt o
f con
curre
ncy
for a
tria
ngle
that
can
be
foun
d at
the
inte
rsec
tion
of th
e th
ree
altit
udes
of t
he
trian
gle.
Exa
mpl
e:
Para
llel (
Bas
es)
Two
base
s of
a th
ree-
dim
ensi
onal
figu
re th
at li
e in
par
alle
l pla
nes.
All
altit
udes
bet
wee
n th
e ba
ses
are
cong
ruen
t.
Para
llel (
Line
s or
Lin
e Se
gmen
ts)
Two
dist
inct
line
s th
at a
re in
the
sam
e pl
ane
and
neve
r int
erse
ct. O
n a
coor
dina
te g
rid, t
he li
nes
have
the
sam
e sl
ope
but d
iffer
ent y
-inte
rcep
ts. T
hey
are
alw
ays
the
sam
e di
stan
ce a
part
from
eac
h ot
her.
Par
alle
l lin
e se
gmen
ts a
re s
egm
ents
of p
aral
lel l
ines
. The
sym
bol f
or p
aral
lel i
s ||
(e.g
., A
B|| C
D is
read
“lin
e se
gmen
t AB
is p
aral
lel t
o lin
e se
gmen
t CD
”).
Para
llel (
Plan
es)
Two
dist
inct
pla
nes
that
nev
er in
ters
ect a
nd a
re a
lway
s th
e sa
me
dist
ance
apa
rt.
Para
llel (
Side
s)
Two
side
s of
a tw
o-di
men
sion
al fi
gure
that
lie
on p
aral
lel l
ines
.
K
eyst
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Exam
s: G
eom
etry
Ass
essm
ent
An
chor
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ligi
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t G
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ary
Jan
uar
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01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
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tion
Page
18
Ja
nuar
y 20
13
Para
llelo
gram
A
qua
drila
tera
l who
se o
ppos
ite s
ides
are
par
alle
l and
con
grue
nt (i
.e.,
ther
e ar
e tw
o pa
irs o
f par
alle
l si
des)
. Ofte
n on
e pa
ir of
thes
e op
posi
te s
ides
is lo
nger
than
the
othe
r pai
r. O
ppos
ite a
ngle
s ar
e al
so
cong
ruen
t, an
d th
e di
agon
als
bise
ct e
ach
othe
r. E
xam
ple:
pa
ralle
logr
am
Perim
eter
Th
e to
tal d
ista
nce
arou
nd a
clo
sed
figur
e. F
or a
pol
ygon
, it i
s th
e su
m o
f the
leng
ths
of it
s si
des.
Perp
endi
cula
r Tw
o lin
es, s
egm
ents
, or r
ays
that
inte
rsec
t, cr
oss,
or m
eet t
o fo
rm a
90°
or r
ight
ang
le. T
he p
rodu
ct o
f th
eir s
lope
s is
– 1 (i.
e., t
heir
slop
es a
re “n
egat
ive
reci
proc
als”
of e
ach
othe
r). T
he s
ymbo
l for
pe
rpen
dicu
lar i
s ⊥
(e.g
., ⊥
AB
CD
is re
ad “l
ine
segm
ent A
B is
per
pend
icul
ar to
line
seg
men
t CD
”). B
y de
finiti
on, t
he tw
o le
gs o
f a ri
ght t
riang
le a
re p
erpe
ndic
ular
to e
ach
othe
r.
Perp
endi
cula
r Bis
ecto
r A
line
that
inte
rsec
ts a
line
seg
men
t at i
ts m
idpo
int a
nd a
t a ri
ght a
ngle
.
π (P
i) Th
e ra
tio o
f the
circ
umfe
renc
e of
a c
ircle
to it
s di
amet
er. I
t is
3.14
1592
65…
to 1
or s
impl
y th
e va
lue
3.14
1592
65…
. It c
an a
lso
be u
sed
to re
late
the
radi
us o
f a c
ircle
to th
e ci
rcle
’s a
rea.
It is
ofte
n
appr
oxim
ated
usi
ng e
ither
3.1
4 or
22 7.
K
eyst
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Exam
s: G
eom
etry
Ass
essm
ent
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chor
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ligi
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Page
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Ja
nuar
y 20
13
Plan
e A
set
of p
oint
s th
at fo
rms
a fla
t sur
face
that
ext
ends
infin
itely
in a
ll di
rect
ions
. It h
as n
o he
ight
.
Plot
ting
Poin
ts
To p
lace
poi
nts
on a
coo
rdin
ate
plan
e us
ing
the
x-co
ordi
nate
s an
d y-
coor
dina
tes
of th
e gi
ven
poin
ts.
Poin
t A
figu
re w
ith n
o di
men
sion
s—it
has
no le
ngth
, wid
th, o
r hei
ght.
It is
gen
eral
ly in
dica
ted
with
a s
ingl
e do
t an
d is
labe
led
with
a s
ingl
e le
tter o
r an
orde
red
pair
on a
coo
rdin
ate
plan
e. E
xam
ple:
●P
poin
t P
Poly
gon
A c
lose
d pl
ane
figur
e m
ade
up o
f thr
ee o
r mor
e lin
e se
gmen
ts (i
.e.,
a un
ion
of li
ne s
egm
ents
con
nect
ed
end
to e
nd s
uch
that
eac
h se
gmen
t int
erse
cts
exac
tly tw
o ot
hers
at i
ts e
ndpo
ints
); le
ss fo
rmal
ly, a
flat
sh
ape
with
stra
ight
sid
es. T
he n
ame
of a
pol
ygon
des
crib
es th
e nu
mbe
r of s
ides
/ang
les
(e.g
., tri
angl
e ha
s th
ree
side
s/an
gles
, a q
uadr
ilate
ral h
as fo
ur, a
pen
tago
n ha
s fiv
e, e
tc.).
Exa
mpl
es:
po
lygo
ns
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
20
Ja
nuar
y 20
13
Poly
hedr
on
A th
ree-
dim
ensi
onal
figu
re o
r sol
id w
hose
flat
face
s ar
e al
l pol
ygon
s w
here
all
edge
s ar
e lin
e se
gmen
ts.
It ha
s no
cur
ved
surfa
ces
or e
dges
. The
plu
ral i
s “p
olyh
edra
.” E
xam
ples
:
po
lyhe
dra
Pris
m
A th
ree-
dim
ensi
onal
figu
re o
r pol
yhed
ron
that
has
two
cong
ruen
t and
par
alle
l fac
es th
at a
re p
olyg
ons
calle
d ba
ses.
The
rem
aini
ng fa
ces,
cal
led
late
ral f
aces
, are
par
alle
logr
ams
(ofte
n re
ctan
gles
). If
the
late
ral f
aces
are
rect
angl
es, t
he p
rism
is c
alle
d a
“righ
t pris
m”;
othe
rwis
e, it
is c
alle
d an
“obl
ique
pris
m.”
Unl
ess
othe
rwis
e sp
ecifi
ed, i
t may
be
assu
med
all
pris
ms
are
right
pris
ms.
Pris
ms
are
nam
ed b
y th
e sh
ape
of th
eir b
ases
. Exa
mpl
es:
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
21
Ja
nuar
y 20
13
Proo
f by
Con
trad
ictio
n A
set
of s
tate
men
ts u
sed
to d
eter
min
e th
e tru
th o
f a p
ropo
sitio
n by
sho
win
g th
at th
e pr
opos
ition
bei
ng
untru
e w
ould
impl
y a
cont
radi
ctio
n (i.
e., o
ne a
ssum
es th
at w
hat i
s tru
e is
not
true
, the
n, e
vent
ually
one
di
scov
ers
som
ethi
ng th
at is
cle
arly
not
true
; whe
n so
met
hing
is n
ot n
ot-tr
ue, t
hen
it is
true
). It
is
som
etim
es c
alle
d th
e “la
w o
f dou
ble
nega
tion.
”
Prop
ortio
nal R
elat
ions
hip
A re
latio
nshi
p be
twee
n tw
o eq
ual r
atio
s. It
is o
ften
used
in p
robl
em s
olvi
ng s
ituat
ions
invo
lvin
g si
mila
r fig
ures
.
Pyra
mid
A
thre
e-di
men
sion
al fi
gure
or p
olyh
edro
n w
ith a
sin
gle
poly
gon
base
and
tria
ngul
ar fa
ces
that
mee
t at a
si
ngle
poi
nt o
r ver
tex.
The
face
s th
at m
eet a
t the
ver
tex
are
calle
d la
tera
l fac
es. T
here
is th
e sa
me
num
ber o
f lat
eral
face
s as
ther
e ar
e si
des
of th
e ba
se. T
he s
horte
st d
ista
nce
from
the
base
to th
e ve
rtex
is c
alle
d th
e al
titud
e. If
the
altit
ude
goes
thro
ugh
the
cent
er o
f the
bas
e, th
e py
ram
id is
cal
led
a “ri
ght
pyra
mid
”; ot
herw
ise,
it is
cal
led
an “o
bliq
ue p
yram
id.”
Unl
ess
othe
rwis
e sp
ecifi
ed, i
t may
be
assu
med
all
pyra
mid
s ar
e rig
ht p
yram
ids.
A p
yram
id is
nam
ed fo
r the
sha
pe o
f its
bas
e (e
.g.,
trian
gula
r pyr
amid
or
squa
re p
yram
id).
Exa
mpl
e:
Pyth
agor
ean
Theo
rem
A
form
ula
for f
indi
ng th
e le
ngth
of a
sid
e of
a ri
ght t
riang
le w
hen
the
leng
ths
of tw
o si
des
are
give
n. It
is
a2 + b
2 = c
2 , whe
re a
and
b a
re th
e le
ngth
s of
the
legs
of a
righ
t tria
ngle
and
c is
the
leng
th o
f the
hy
pote
nuse
.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
22
Ja
nuar
y 20
13
Qua
drila
tera
l A
four
-sid
ed p
olyg
on. I
t can
be
regu
lar o
r irre
gula
r. Th
e m
easu
res
of it
s fo
ur in
terio
r ang
les
alw
ays
add
up to
360
°.
Rad
ius
(of a
Circ
le)
A li
ne s
egm
ent t
hat h
as o
ne e
ndpo
int a
t the
cen
ter o
f the
circ
le a
nd th
e ot
her e
ndpo
int o
n th
e ci
rcle
. It i
s th
e sh
orte
st d
ista
nce
from
the
cent
er o
f a c
ircle
to a
ny p
oint
on
the
circ
le. I
t is
half
the
leng
th o
f the
di
amet
er. T
he p
lura
l is
“radi
i.” E
xam
ple:
Ray
A
par
t or p
iece
of a
line
with
one
fixe
d en
dpoi
nt. F
orm
ally
, it i
s th
e en
dpoi
nt a
nd a
ll po
ints
in o
ne
dire
ctio
n. T
he ra
y A
B is
writ
ten
, whe
re A
is a
n en
dpoi
nt o
f the
ray
that
pas
ses
thro
ugh
poin
t B.
Exa
mpl
e:
ra
y A
B (
)
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
23
Ja
nuar
y 20
13
Rec
tang
ular
Pris
m
A th
ree-
dim
ensi
onal
figu
re o
r pol
yhed
ron
whi
ch h
as tw
o co
ngru
ent a
nd p
aral
lel r
ecta
ngul
ar b
ases
. In
form
ally
, it i
s a
“box
sha
pe” i
n th
ree
dim
ensi
ons.
Exa
mpl
e:
Reg
ular
Pol
ygon
A
pol
ygon
with
sid
es a
ll th
e sa
me
leng
th a
nd a
ngle
s al
l the
sam
e si
ze (i
.e.,
all s
ides
are
con
grue
nt o
r eq
uila
tera
l, an
d al
l ang
les
are
cong
ruen
t or e
quia
ngul
ar).
Exa
mpl
e:
re
gula
r pol
ygon
Rig
ht A
ngle
A
n an
gle
that
mea
sure
s ex
actly
90°
.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
24
Ja
nuar
y 20
13
Rig
ht T
riang
le
A tr
iang
le w
ith o
ne a
ngle
that
mea
sure
s 90
° (i.
e., i
t has
one
righ
t ang
le a
nd tw
o ac
ute
angl
es).
The
side
op
posi
te th
e rig
ht a
ngle
is c
alle
d th
e hy
pote
nuse
and
the
two
othe
r sid
es a
re c
alle
d th
e le
gs.
rig
ht tr
iang
le A
BC
Scal
ene
Tria
ngle
A
tria
ngle
that
has
no
cong
ruen
t sid
es (i
.e.,
the
thre
e si
des
all h
ave
diffe
rent
leng
ths)
. The
tria
ngle
als
o ha
s no
con
grue
nt a
ngle
s (i.
e., t
he th
ree
angl
es a
ll ha
ve d
iffer
ent m
easu
res)
.
Seca
nt (o
f a C
ircle
) A
line
, lin
e se
gmen
t, or
ray
that
pas
ses
thro
ugh
a ci
rcle
at e
xact
ly tw
o po
ints
. The
seg
men
t of t
he s
ecan
t co
nnec
ting
the
poin
ts o
f int
erse
ctio
n is
a c
hord
of t
he c
ircle
. Exa
mpl
e:
se
cant
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
25
Ja
nuar
y 20
13
Sect
or (o
f a C
ircle
) Th
e ar
ea o
r reg
ion
betw
een
an a
rc a
nd tw
o ra
dii a
t eith
er e
nd o
f tha
t arc
. The
two
radi
i div
ide
or s
plit
the
circ
le in
to tw
o se
ctor
s ca
lled
a “m
ajor
sec
tor”
and
a “m
inor
sec
tor.”
The
maj
or s
ecto
r has
a c
entra
l ang
le
of m
ore
than
180
°, w
here
as th
e m
inor
sec
tor h
as a
cen
tral a
ngle
of l
ess
than
180
°. It
is s
hape
d lik
e a
slic
e of
pie
. Exa
mpl
e:
Segm
ent (
of a
Circ
le)
The
area
or r
egio
n be
twee
n an
arc
and
a c
hord
of a
circ
le. I
nfor
mal
ly, t
he a
rea
of a
circ
le “c
ut o
ff” fr
om
the
rest
by
a se
cant
or c
hord
. Exa
mpl
e:
Sem
icirc
le
A h
alf o
f a c
ircle
. A 1
80°
arc.
For
mal
ly, a
n ar
c w
hose
end
poin
ts li
e on
the
diam
eter
of t
he c
ircle
.
Shap
e S
ee fi
gure
.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
26
Ja
nuar
y 20
13
Side
O
ne o
f the
line
seg
men
ts w
hich
mak
e a
poly
gon
(e.g
., a
pent
agon
has
five
sid
es).
The
endp
oint
s of
a
side
are
ver
tices
of t
he p
olyg
on.
Sim
ilar F
igur
es
Figu
res
havi
ng th
e sa
me
shap
e, b
ut n
ot n
eces
saril
y th
e sa
me
size
. Ofte
n, o
ne fi
gure
is th
e di
latio
n (“e
nlar
gem
ent”)
of t
he o
ther
. For
mal
ly, t
heir
corre
spon
ding
sid
es a
re in
pro
porti
on a
nd th
eir
corre
spon
ding
ang
les
are
cong
ruen
t. W
hen
sim
ilar f
igur
es a
re n
amed
, the
ir co
rresp
ondi
ng v
ertic
es a
re
liste
d in
the
sam
e or
der (
e.g.
, if t
riang
le A
BC
is s
imila
r to
trian
gle
XYZ,
then
ver
tex
C c
orre
spon
ds to
ve
rtex
Z). E
xam
ple:
Δ
AB
C is
sim
ilar t
o Δ
XYZ
Sine
(of a
n An
gle)
A
trig
onom
etric
ratio
with
in a
righ
t tria
ngle
. The
ratio
is th
e le
ngth
of t
he le
g op
posi
te th
e an
gle
to th
e le
ngth
of t
he h
ypot
enus
e of
the
trian
gle.
sine
of a
n an
gle
= le
ngth
of o
ppos
ite le
gle
ngth
of h
ypot
enus
e
Skew
Lin
es
Two
lines
that
are
not
par
alle
l and
nev
er in
ters
ect.
Ske
w li
nes
do n
ot li
e in
the
sam
e pl
ane.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
27
Ja
nuar
y 20
13
Sphe
re
A th
ree-
dim
ensi
onal
figu
re o
r sol
id th
at h
as a
ll po
ints
the
sam
e di
stan
ce fr
om th
e ce
nter
. Inf
orm
ally
, a
perfe
ctly
roun
d ba
ll sh
ape.
Any
cro
ss-s
ectio
n of
a s
pher
e is
circ
le. E
xam
ple:
sp
here
Stra
ight
Ang
le
An
angl
e th
at m
easu
res
exac
tly 1
80°.
Surf
ace
Area
Th
e to
tal a
rea
of th
e su
rface
of a
thre
e-di
men
sion
al fi
gure
. In
a po
lyhe
dron
, it i
s th
e su
m o
f the
are
as o
f al
l the
face
s (i.
e., t
wo-
dim
ensi
onal
sur
face
s).
Tang
ent (
of a
Circ
le)
A li
ne, l
ine
segm
ent,
or ra
y th
at to
uche
s a
circ
le a
t exa
ctly
one
poi
nt. I
t is
perp
endi
cula
r to
the
radi
us a
t th
at p
oint
. Exa
mpl
e:
is
a ta
ngen
t of c
ircle
O
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
28
Ja
nuar
y 20
13
Tang
ent (
of a
n A
ngle
) A
trig
onom
etric
ratio
with
in a
righ
t tria
ngle
. The
ratio
is th
e le
ngth
of t
he le
g op
posi
te th
e an
gle
to th
e le
ngth
of t
he le
g ad
jace
nt to
the
angl
e.
tang
ent o
f an
angl
e =
leng
th o
f opp
osite
leg
leng
th o
f adj
acen
t leg
Tang
ent (
to a
Circ
le)
A p
rope
rty o
f a li
ne, l
ine
segm
ent,
or ra
y th
at it
touc
hes
a ci
rcle
at e
xact
ly o
ne p
oint
. It i
s pe
rpen
dicu
lar t
o th
e ra
dius
at t
hat p
oint
. Exa
mpl
e:
is
tang
ent t
o ci
rcle
O a
t poi
nt P
Thre
e-D
imen
sion
al F
igur
e A
figu
re th
at h
as th
ree
dim
ensi
ons:
leng
th, w
idth
, and
hei
ght.
Thre
e m
utua
lly p
erpe
ndic
ular
dire
ctio
ns
exis
t.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
29
Ja
nuar
y 20
13
Tran
sver
sal
A li
ne th
at c
ross
es tw
o or
mor
e lin
es in
ters
ectin
g ea
ch li
ne a
t onl
y on
e po
int t
o fo
rm e
ight
or m
ore
angl
es. T
he li
nes
that
are
cro
ssed
may
or m
ay n
ot b
e pa
ralle
l. E
xam
ple:
lin
e f i
s a
trans
vers
al th
roug
h pa
ralle
l lin
es l
and
m
Trap
ezoi
d A
qua
drila
tera
l with
one
pai
r of p
aral
lel s
ides
, whi
ch a
re c
alle
d th
e ba
ses.
Tria
ngle
A
thre
e-si
ded
poly
gon.
The
mea
sure
s of
its
thre
e in
terio
r ang
les
add
up to
180
°. T
riang
les
can
be
cate
goriz
ed b
y th
eir a
ngle
s, a
s ac
ute,
obt
use,
righ
t, or
equ
iang
ular
; or b
y th
eir s
ides
, as
scal
ene,
is
osce
les,
or e
quila
tera
l. A
poi
nt w
here
two
of th
e th
ree
side
s in
ters
ect i
s ca
lled
a ve
rtex.
The
sym
bol f
or
a tri
angl
e is
Δ (e
.g.,
ΔAB
C is
read
“tria
ngle
ABC
”).
Trig
onom
etric
Rat
io
A ra
tio th
at c
ompa
res
the
leng
ths
of tw
o si
des
of a
righ
t tria
ngle
and
is re
lativ
e to
the
mea
sure
of o
ne o
f th
e an
gles
in th
e tri
angl
e. T
he c
omm
on ra
tios
are
sine
, cos
ine,
and
tang
ent.
Two-
Dim
ensi
onal
Fig
ure
A fi
gure
that
has
onl
y tw
o di
men
sion
s: le
ngth
and
wid
th (n
o he
ight
). Tw
o m
utua
lly p
erpe
ndic
ular
di
rect
ions
exi
st. I
nfor
mal
ly, i
t is
“flat
look
ing.
” The
figu
re h
as a
rea,
but
no
volu
me.
K
eyst
one
Exam
s: G
eom
etry
Ass
essm
ent
An
chor
& E
ligi
ble
Con
ten
t G
loss
ary
Jan
uar
y 2
01
3
Pe
nnsy
lvan
ia D
epar
tmen
t of E
duca
tion
Page
30
Ja
nuar
y 20
13
Vert
ex
A p
oint
whe
re tw
o or
mor
e ra
ys m
eet,
whe
re tw
o si
des
of a
pol
ygon
mee
t, or
whe
re th
ree
(or m
ore)
ed
ges
of a
pol
yhed
ron
mee
t; th
e si
ngle
poi
nt o
r ape
x of
a c
one.
The
plu
ral i
s “v
ertic
es.”
Exa
mpl
es:
Volu
me
The
mea
sure
, in
cubi
c un
its o
r uni
ts3 , o
f the
am
ount
of s
pace
con
tain
ed b
y a
thre
e-di
men
sion
al fi
gure
or
solid
(i.e
., th
e nu
mbe
r of c
ubic
uni
ts it
take
s to
fill
the
figur
e).
Zero
Ang
le
An
angl
e th
at m
easu
res
exac
tly 0
°.
Cover photo © Hill Street Studios/Harmik Nazarian/Blend Images/Corbis.
Copyright © 2013 by the Pennsylvania Department of Education. The materials contained in this publication may be
duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the duplication
of materials for commercial use.
Keystone Exams: Geometry
Assessment Anchors and Eligible Contentwith Sample Questions and Glossary
January 2013