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NAME
DATE
PERIOD
Practice
0)c-1-10
Bisectors, Medians, and Altitudes
4,
ALGEBRA In EABC, BF is the angle bisector of LABC, AE, BF,
and CD are medians, and P is the centroid.
1. Find x if DP = 4x — 3 and CP = 30.
2. Find y if AP = y and EP = 18.
3. Find z if FP = 5z + 10 and BP = 42.
f inZABC = x and mLBAC = mLBCA = 2x — 10, is BF an altitude? Explain.
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reasons. PI.
Pac, is tsoscetes so ?F
is an anck &sec-for
also an a.114thxte4Seconcii
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4143P ----po, yy,4ep(.--- ---70 1
ALGEBRA In APRS, PT is an altitude and PX is a median.
Stance=
54- Up
/fin SW
W
so vinLAFB=cia
ind RS if RX = x + 7 and SX = 3x — 11.
is
ro-ect pan 12 7(-SX so 5X -11 =+-7
2.x=sx= r?_:R,s=
ind RT if RT = x — 6 and mLPTI? = 8x — 6.
Copyright ©G lencoe/McGraw-HiII, a division of The McGraw- HillCompan ies, Inc.
x+7
3)(--11
,(:c7TR-z-_clo° so
x-(o=c10 and x I
An5Loeir; i
RT.= x-C9 t)-nc\ X= laZ-7=-:
-(0 77-F
s
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ALGEBRA In ADEF, GI is a perpendicular bisector.
•
XT
E
()Find x if EH = 16 and FH = 6x — 5.
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up : 614 =PI4 SO I to= (0)( - 6
answer: a(= 3, 5
8. Find y if EG = 3.2y — 1 and FG = 2y + 5.
z if mLEGH = 12z.
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COORDINATE GEOMETRY The vertices of ASTU are S(0, 1), T(4, 7), and U(8, —3).
Find the coordinates of the points of concurrency of ASTU.
10. orthocenter
12. circumcenter
11. centroid
13. MOBILES Nabuko wants to construct a mobile out of flat triangles so that the surfaces
of the triangles hang parallel to the floor when the mobile is suspended. How can
Nabuko be certain that she hangs the triangles to achieve this effect?
Chapter 5
29
Glencoe Geometry
PERIOD
DATE
NAME
Practice
Inequalities and Triangles
Determine which angle has the greatest measure.
1, L3, L4
2. L4, L8, L9
4 1 bee.au h ary+erwr 4 6 ferk4er-.
e 4.YY\04-<
1r\ vr\
nj\eS
L7, L8, L10
6L2, L3, -1--her)
L7
SaMC
reaso,n
-*I
Use the Exterior Angle Inequality Theorem to list
all angles that satisfy the stated condition.
all angles whose measures are less than mL1
.43 1 </--\)
Z1 )
6. all angles whose measures are less than mL3
5
all angles whose measures are greater than mL7
3/---Ii 4. 1--5 ) 49
)
8. all angles whose measures are greater than mL2
LQRW, mLRWQ
(R.\).) is across
f-yum
mLRST, mLTRS
so
10. mLRTW, mLTWR
;I:irr)
5a
yvl
01TS -ProTA Q";
IZST is acroSS °•‘e0tY) 12)5 0,r‘\ <TRS is 0,
So vv\ < IZST > ne\411Z3
Determine
re a ion
of the given sides.
DH, GH
0,/ 0265' Pvoyyl
So_11:514
agd
14. DE, DG
3a ° ate GI 14 15 OtrOSS fill' V4?
00
aro F'6.1 IS ClomsS PYOrn
SPORTS Tfie figure s ows • position of three trees on one
part of a FrisbeeTM course. At which tree position is the angle
between the trees the greatest?
is 9 reaks#
Chapter 5
17°
16. DE, EG
EG, FG
15 CAC•S
-Fro m
93°
F
engths
b 113
iXCavT
side
30
Is avrDSS
ft
37.5 ft
53 ft
Glencoe Geometry
Copyright© Glencoe/McG raw-Hill ,a divisionof The McG raw-Hill Companies ,I nc .
Determine the relationship between the measures
of the given angles.
Chapter 5 Review Guide!
BILLER
1. Identify AD in each triangle as the median, perpendicular bisector, altitude or angle bisector.
A
A
lots-cc-1-ov-
erpe-narcu
2.
Draw
A
PRS ason acute scalene triangle with PT as the altitude and PX as the median of the
ok.)sInct Pi ts a mea G4n RY
triangle.
)(.=.-ci
x-=--/(Asx- ----a,
\) 4pw-=q00
a.
Find RS if RX=x+7 and SX=3x-11. RS= \ t -VA
b.
Find RT if RTx-6 and m<PTR=8x-6. RT=
`..5
(0
Find z if m<EGH =12z. z=
-EC 14= 9o°
71=-1.5
4.Draw
A AB
with m<A=35' and m<B=125 ° . List the sides from shortest to longest
A
Draw
A
AS? 13C) CA
DEF with sides DE=15, EF=10 and DF=12. List the angles from smallest to greatest.
0
4 D ) Z. 6)
IP
b
GI is a perpendicular bisector. Find x if EH=16 and FH=6x-5. X=
3.
ot.nc\
F
)(-5 -L.- /10
5.Determine the relationship between the measures of the given sides or angles.
<R
<RUSI;
<
All
35 <T <UST 22
<UVS
>
>
AC/
6.
AC
BC
BC
DB
13
DB
V
25
List:
All <s less than m<1 by Exterior < Inequality Theorem:
1J
All <s less than m<9 by Exterior < Inequality Theorem:
All <s greater than m<5 by Exterior < Inequality Theorem:
All <s greater than m<8 by. Exterior < Inequality Theorem:
7.
eS
r,3
4
< 5)
4.3,4.1
Si-L-1)
1-14--11>5
Lti--E5 1 1
4, 8, and 11?
20, 22, and 2?
9.
QQ
Can these measures form a triangle? Why or why not?
2, 3, and 4?
8.
-5
S <-7) <
no
a, o
Find the range for the measure of the third side of the triangle with side lengths:
12 and 23
1\ X <35
37 and 16
6\
IP,-4- g3,>)( —1)3
x
t3
4.- >16
>
4-3s
) 93+-Y>
)(>-)i
>>(.
'&> - a\L
\,0 -\-.)(>3-1
Write the assumption you would make to begin an indirect proof for ti re statements:
"Mrs. Eby loves geometry."
•
"If 5x=10, then x=2."
10. Smile because you LOVE Geometry!!! ©
Sbj
does no 4- love 9-cop
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