Kami Export - ANSWERS%20Geometric%20Proofs%20pkt
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School
Ridge Community High School *
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Course
1093500
Subject
Mathematics
Date
Nov 24, 2024
Type
Pages
5
Uploaded by ConstableHornetMaster75
Name
‘k‘
E
\/
Date
Class
Practice
A
Za
8l
Geometric
Proof
Write
the
letter
of
the
correct
justification
next
to
each
step.
J
I
N\s
(Use
one
justification
twice.)
!
Given:
HJ
is
the
bisector
of
ZIHK
and
£1
=
/3.
e
E3H
1.
HJ
is
the
bisector
of
£IHK.
B
A.
Definition
of
£
bisector
L
L2=21
fi
B.
Given
L.
L1=43
[%
£2=/3
Ina__
1o
-
tolumn
EIESESIN
C.
Transitive
Prop.
of
=
proof,
each
step
in
the
proof
is
on
the
left
and
the
reason
for
the
step
is
on
the
right.
Fill
in
the
blanks
with
the
justifications
and steps
listed
to
complete
the
two-column
proof.
Use
this
list
to
complete
the
proof.
L1=22
Def.
of
straight
£
Z1
and
£2
are
straight
angles.
\K
6.
Given:
Z1
and
£2
are
straight
angles.
/
2,
Prove:
£1=£2
Proof:
Statements
Reasons
fallandl2
Qe
Steanig
i
(}nglig’
1.
Given
2.m«£1=180°
m£2
=
180°
2.b.
_def.
of
S-hmghfé'fi
3.
ms£1=mxsL2
3.
Subst.
Prop.
of
=
4.c.
L=l
T
4.
Def.
of
=
£
Follow
the
plan
to
fill
in
the
blanks
in
the
two-column
proof.
7.
Given:
£1
and
£2
form
a
linear
pair,
and
£3
and
£4
form
a
linear
pair.
Prove:
mZ1
+
mZ£2
+
m4£3
+
m«£4
=
360°
Plan:
The
Linear
Pair
Theorem
shows
that
£1
and
£2
are
supplementary
and
£3
and
£4
are
supplementary.
The
definition
of
supplementary
says
that
mZ£1+m«£2
=180°
and
m«£3
+
m£4
=
180°.
Use
the
Addition
Property
of
Equality
to
make
the
conclusion.
Statements
Reasons
1.
£1
and
£2
form
a
linear
pair,
and
£3
and
£4
form
a
linear
pair.
la
_
(Qive~
J
£3
and
Z4
are
supplementary.
2.
Z1
and
£2
are
supplementary,
and
2b
Lontar
Pair
Thm
.
sl
tmt2=1°
M3+
mlY=1£0
3.
Def.
of
supp.
4
4.
mZ1+m£2
+
m£L3
+
ms£4
=
360°
4.d.
_Add
pmp-
G
=
Original
content
Copyright
©
by
Holt
McDougal.
Additions
and
changes
to
the
original
content
are
the
responsibility
of
the
instructor.
2-43
Holt
Geometry
Name
K
€
\/
Date
Class
Practice
B
28
Geometric
Proof
Write
a
justification
for
each
step.
Given:
AB
=
EF,
B
is
the
midpoint
of
AC,
and
E
is
the
midpoint
of
DF
.
1.
B
is
the
midpoint
of
R,
and
E
is
the
midpoint
of
DF
.
.
AB=BC,and
DE
=EF
.
.
AB=BC,
and
DE
=
EF.
4,
AB+BC=AC,
and
DE
+
EF
=
DF.
5.
2AB=AC,
and
2EF
=
DF.
(o)
.
AB=EF
.
2AB=2EF
o)
.
AC=DF
.
AC=DF
Fill
in
the
blanks
to
complete
the
two-column
proof.
10.
Given:
ZHKJ
is
a
straight
angle.
KI
bisects
ZHKJ.
c)'f
mid
poinT
def.
of
congryent
Seq
.
add.
post
-
s
siHuhen
POE
5
W.{’
n
(
pttu
)
‘l’\flu\lf
.
Poe
Subst.
Poc
def
of
congruenct
Prove:
ZIKJ
is
a
right
angle.
Proof:
Statements
Reasons
t.a._L
HKT
is
g
&atfht
angle
[1.Given
2.
mZHKJ
=
180°
2.b.
__(od{
ot
Shaughht
L
3.0
K1
hoedS
LHKT
3.
Given
4.
ZIKJ
=
ZIKH
4.
Def.
of
£
bisector
5.
mZIKJ
=
mzIKH
5.
Def.
of
=
4
6.d._MLTKT+
M
LT¢H”
m/
HKT
|6
£
Add.
Post.
7.
2mZIKJ
=
180°
7.e.Subst.
(Steps
2
.S,
b
)
8.
m«IKJ
=
90°
8.
Div.
Prop.
of
=
9.
ZIKJis
a
right
angle.
o.f._cuf
of
right
¢
Original
content
Copyright
©
by
Holt
McDougal.
Additions
and
changes
to
the
original
content
are
the
responsibility
of
the
instructor.
2-44
Holt
Geometry
Name
(\
E\/
Date
Class
Practice
C
28
Geometric
Proof
Write
a
two-column
proof.
1.
Given:
The
sum
of
the
angle
measures
in
a
triangle
is
180°.
,
Prove:
m£1=m<3
+
mz4
o
e,
Sty
mend
S
J
usShicainon
o
.
=
2
€N
O
wlL2r4mL3tm
Ld=1%0
(Q
9
W“
—~
o
Q&
2)
gwitin
@
L1
f\,\ath‘»;;r“
=
2
—
0
L
~
5
[ingar
f
N
G/\
Linear
pasl
Thm
(D
LianalZ
are
Q0T
7
ot
of
opp!.
@
mel
Ame2
s
:
@
substriwhon
P06
G
mLZtmi3tmiY=miitmlZ
@/‘
Subtr,
PoE
-
A
4+mLY
=md)
N
T
~
©C:ff
rYl\fYL\LT
=
MLSFTmeY
67
}’.\’
s
POC
2.
Peter
drives
on
a
straight
road
and
stops
at
an
intersection.
The
intersecting
road
is
also
straight.
Peter
notices
that
one
of
the
angles
formed
by
the
intersection
is
a
right
angle.
He
concludes
that
the
other
three
angles
must
also
be
right
angles.
Draw
a
diagram
and
write
a
two-column
proof
to
show
that
Peter
is
correct.
|
X
Skate
mends
&
.,.__VS+\'{{‘
cation
@
il
12l
@)
[j(vUT
i
@/l.‘mfi'(-c‘&
=
/T
.
righ
ANy
\
O
21
vsa
right
angle
@
gree3
S
&
LI
andt2
cre
&
limear
/%.”"(29“’{N
Z
2
andlD
arta
linar
par
(D
subst.
7
|
and!l
d
are
o
lindar
pair
.
e
I
o
Q5>
/3
1SAa
B
Ll
analZ
art
Supp!
B
Linsa
|
orightt
’
L2
andl
Sare
Sv’lflp'.
f
(‘3,
(U‘[
o
LL
ane
l
¥4
areig-;}apl.
@
[)(JZ/-U/\SU'OPL
'
o
,(}-hf[,
B
wiiAmi2
=18
.
mL2
t
mL
2@
/g(c))e;
.
O
B
j
-
mL
l,
.4
(TC?
l
)
def.
of
r/ifq‘(
=
B
%
Z;C%l
"
mLZ
=160°
(D/
Su
bstrhcon
RO
s
Y
2
b
c
,
-
[
€
OU
—
i
(‘0
1
'“LL/'
)
Ig
/‘(AOG
C’)\/
S
b‘f'Y_
POC
A
me2=q0°
el
10
—n
T
okt
L)
LQ@
L2
and
L4
Gre
rght
L's®)
ded.
of
mght
L's
riginal
content
Copyright
©
by
Holt
McDougal.
Additions
and
changes
to
the
original
content
are
the
responsibility
of
the
instructor.
@\)
L
P
R
are
yertieald
'S
2-45
(G)
Gve
o
:
Holt
Geometry
(o
/1%
/13
i
ouf.
of
verticel
LS
|
)
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Name
)
K
E
y
Date
Class
Problem
Solving
Y2
Geometric
Proof
1.
Refer
to
the
diagram
of
the
stained-glass
window
and
use
the
given
plan
to
write
a
two-column
proof.
Given:
Z1
and
£3
are
supplementary.
£2
and
£4
are
supplementary.
L3=/4
‘
b
Prove:
Z1=./2
4
|
%
Plan:
Use
the
definition
of
supplementary
angles
to
write
\;
y
the
given
information
in
terms
of
angle
measures.
Then
use
the
Substitution
Property
of
Equality
and
the
Subtraction
Property
of
Equality
to
conclude
that
£1
=
22,
‘
@)
o
il
Y
4
&L}DP"
(’:”
(j‘(\ffl,\,
LZ,
LY
are
SUPF',
"
‘
|
(2
melrmL-
1
80°
@
deof
)
Spp'.
=
1§0°
mcel?
miYy
=l
.
B
)
2
=mL2
¥y
(’)
sl
St
-
POE
é”mLI\‘rnc%
M
A
é
L3=L4
@/Cj'\l’e.o\
p
(s%
me3
=med
6’/
(fi{f‘o.'
1%5
T‘\/
Y=
me2+mey
Q:)
Su
ST
-
Q)
Sdlotr
.
prop
of
553
®
dod
(8
(cmg‘r
The
position
of
a
sprinter
at
the
starting
blocks
is
shown
in
the
diagram.
Which
statement
can
be
proved
using
the
given
information?
Choose
the
best
answer.
2.
Given:
Z1
and
£4
are
right
angles.
A
£3=/45
C
m4£1+m«4
=90°
B1=s4
)
D
ms3+ms5=180°
3.
Given:
£2
and
£3
are
supplementary.
£2
and
£5
are
supplementary.
/‘
\/
H
43
and
£5
are
complementary.
J
Z1
and
£2
are
supplementary.
Original
content
Copyright
©
by
Holt
McDougal.
Additions
and
changes
to
the
original
content
are the
responsibility
of
the
instructor.
2-49
Holt
Geometry
Name
K
l:
\;
Date
Class
Challenge
L2l
Prove
It!
In
a
proof,
you
can
often
determine
the
Given
information
from
the
figure.
Write
the
information
that
is
given
in
each
figure.
Then
make
a
conjecture
about
what
you
could
prove
using
the
given
information
oA
Guen:
L1214
JABC
savigni
L
__Guen:
£F
ZET,
F6=TH
Du
ovt:
L2
=
L
3
(answeds
Prove
-
E—flH
=
E—'—j
|’Y\At1
V-
fd
)
3.
Write
a
two-column
proof.
@
P
i
Given:
ZKLM
and
ZNML
are
right
angles.
£2=/3
Prove:
/1=z=/4
-
L‘2
3“M
O
LKLM
,
LUML
are
nghtl's
@
g\e~
Q
L
KLM
ELNML
@
Light
L
Thm,
B
mLKLM
=
mLNML
Ll
e
gt
é\)
M
L
KLM=mel
ime
2
©
angle
acd
.
pait
.
LY
MMM
ZmedTm
|
Q
Subst.
prop-Pph-
.
(6;
Glvein
O
L2223
=7
~
O
mers
e
uit
6)
mMLr+me2
=
mMe2
+tmeH
(®)
Sub
]
X
m
@
Subtr.
Po€
@
|
=
mlLYy
(©
nza/
&Ly
(D
sty
&
©)
et
#mea
2mestmed
Original
content
Copyright
©
by
Holt
McDougal.
Additions
and
changes
to
the
original
content
are
the
responsibility
of
the
instructor.
2-48
Holt
Geometry