5.5 rrianste Inequalih/
ReAd Affd TnY
Name
ong[e [s ocnoss from the longest side of o.
of
srno!1g.p,,3---q-ngfe 6s oenoss fnom fhe 5,|1ps$q5f "s!$e,
i Thesnerm: The Sergest
: fricngle omd the
Exomple 1 List the#nglgs f
,
I
4f'1 ,LL, dF'
.o^ffi
to
lorEesf'
*
'
2.7
"
,
4.3 is across from <L
is the shortest side of the triangle'
2.7 is across from <M'
5.8 is across from <K.
in order from smallest to largest is
ffingles
You try this one: l-ist the angles from
sffile-st to lgfSeS"Eo
d-T * a F, a* F'''
Example
2
List the angles from
largest to smaElest'
<E has to be the largest angle because it is obtuse'
<D is the smallest angle because it is across from x (x
is smaller than 3x,
<D, <C, <E
Try this one: List the angles from*larg-est to snrallest
-t'' / i"i Lb
-,r
i***l*"
E-
"'
t{n ,*'''
\
\r.h "i {
I
e.* rIS
,*';:
d
(:r.
ta^
Example
3: List the sides of the triangle in order from shoctest to Eomgest.
l$0
-15
-1.5
.r1
Uu
Find the 3'd angle of the triangle: 180-45-75=60
The smallest angle is 45, it is across from MN.
The middle angle is 60, it is across from ON.
The largest angle is75, it is across from MO
o
o
o
Ma
ffi-g:t"=$
*
tD
So in order shoftest to longest: MfS, Gt{, M@
Try this one: List the sides of the triangle in order from shodest
III
ts
Y
to longest.
Irc
'#rW
fd $-tr, c[
;
i
Triongle Ineguolity Theonem:
The surn of ony two sides of o tniongle is greater thom the third side"
\.
Exomple 4:
o. Can o friongle hove sides with lengths 2, 3, end 6? F--, N ln \
NO A+3=b ) l\ V O
").r
b. Ccn a trfaargle hove sidgs_with lengthr J
end 15?&'-"'
,*o I f,
rHS
{ t';
WORK: 11+12=?3, 23 is mor.e...thon 15(
side) it+ tfr
WORK:
2+3=5, since 5 is less thon 6
t?+15=27, 27 is more thori-lrftfhe third side)
t1+15=26, 26 is more thgn"1Z(the thir'4side)
Since alt were more thon the
c.
thid
side, YES
9, 10, ond 19?+
\
9*10=19, since the rhird-r,rilo Q + lD = th
Con o triongle hove sides with lengths
woRK:
YffiEL
N0l,
l/i7
rb
Try these:
e.
b"
eom o friorrgle have lemgfhs4,
4-
V, E?-
--
Csrn
\(! q I
\
}Et'
= lt/
{tl
o triongle hove lemgths _6;)_$, TV? d'."--.^. ....-."
hif,
t t"
.,,qt*
i
1r+},t}
c. Com c triongle hove lengths 4,_5, 9? {
1 }1 ;":
i."
:'"t
Ll:
r i
ExompBe
..
E
#
;
5: A tniongle hos sides of lerrgth I
snd 12" What one
Benrgths for the third side?
5o like the previous problem, the sum of ony two sides is mrore thon the
fhird....gives us:
8*12>x
ond 12+x>8
E*x> I 2
x>-4 (fhis gives mo imfo)
2O>x
x>4
x< 20
the possible
Solving
Putting
it together 4<x<20
EASY wcy to
Ia- g = L{
\/x
tAt&aa6
get the onswer!!! 1.2-8
=4
L2+$=Qg
So write os 4<x<20
1ao
Exomple 6: A tricngle hos sides of length 5 on4_16. Wlnot are
the possible lengths for the thind side?
l3;3=ll
ltg-5=lt
I tpr'-'5=&l
5o our sides ore between 11. ond 2l....write
try:
A triongle has sides of length
,{
lengths for the third side?
d'I
You
I
L
-,""*
6
it this woy 1t<x<21
and
7.
Whot ore the possibte
*1 xL3ffi:
"*l *{ I
f
fl
i '{-
d oas sro i- -,rndvd{
iPfl--.'LL
q--1
t
L#
doel no|
t rT rrtv d.8.
l?
t4