statementreason e g h f given alt. int
TRANSCRIPT
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Statement Reason
E G
HF
Given
Given
Alt. Int. <s Thm.
Reflex. Prop of
p.244ex4
SAS. Steps 1,3,4
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Statement Reason
J
K L
M
p.246ex4
Given
Given
Reflex. Prop of ≅
<JKL≅<MLK
SAS Steps 1,2,3
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Statement Reason
p.244 ex 4
A
B C
D
Given
Alt. Int. <s Thm.
Given
SAS Steps 3,2,4
Reflexive Prop of ≅
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Statement Reason
Given: <ZVY≅<WYV, <ZVW≅<WYZ,VW≅YZ
Prove:
V
Y
X
W
Z
p.247: 21
Given
Def. of ≅
m<WVY = m<ZYV
Def. of ≅
Given
SAS, Steps 6,5,7
<ZVY≅<WYV, <ZVW≅<WYZ
m <ZVY = m <WYV,m <ZVW = m <WYZ
m <ZVY + m <ZVW = m <WYV + m <WYZ
<WVY≅ <ZYV
Reflex. Prop of ≅
<Add. Prop of =
<Add. Post
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Determine if you can use ASA to prove the triangles congruent. Explain.
No, no included side
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p. 246:13
Given: B is the midpoint of
A
B CD
B is the mdpt of DC
Given
Given
Def. Mdpt.
SAS Steps2,4,5
Reflex. Propof ≅
<ABD and <ABC areright <s
<ABD≅<ABC
Statement Reason
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Statement Reason
Determine if you can use ASA to prove ΔUVX≅ΔWVX. Explain. p.253ex2X
UV
W
<WVX is a right angle
<UXV ≅ <WXV
given
given
Reflex. Prop
Def. of LinearPair
<WVX ≅ <UVX
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1000
Given:
What is the measure of y?
y
l
m
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Determine if you can use ASA to prove ΔNKL≅ΔLMN. Explain.
p.253ex2
KL
MN
By Alt. Int. <s Thm,
<KLN≅<MNL
Reflex. Prop
No other congruence relationships can be determined, so ASA cannot be applied.
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Determine is you can use the HL Congruence Theorem to prove the triangles congruent.If not, tell what else you need to know.
p.255ex4
Yes No, need the hyp ≅
Yes
It is given that segment AC ≅ segment DB.
Seg. CB ≅ Seg. CB, by the Reflexive Prop.
Since <ABC and <DCB are rt <s, ΔABC and ΔDCB are rt triangles.
ΔABC≅ΔDCB by HL.
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Statement Reason
Given: <G≅ <K, <J≅<M, HJ≅LMProve: ΔGHJ≅ΔKLM H
K
L
M
G J
p.254ex3
Given
Given
ASA Steps1,3,2
Third <s Thm
ΔGHJ ≅ ΔKLM
<H ≅ <L
<G ≅ <K, <J ≅ <M
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Statement Reason
p.254ex3
Y
WZ VX
Use AAS to prove the triangles congruent.
Given: <X ≅ <V, <YZW ≅ <YWZ,
Prove: ΔXYZ≅ΔVYW
<X ≅ <V
<YZW ≅ <YWZ
AAS
Given
Given
Given
≅ Supps Thm
Def. of Supp <s
Def. of Supp <s
<XZY is suppto <YZW
<YWX is supp to <VWY
<YZX ≅ <YWV
≅XYZ ≅ ΔVYW
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Statement Reason
AB
DE
F
C
Given:
Prove:
p. 257: 13
Given
Rt. < ≅Thm
GivenGiven
AAS
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Statement Reason
p.257:15
Given: E is a midpoint of Segments AD and BCProve: Triangles ABE and DCE are congruent A
B
C
D
E
<A and <D are rt anglesGiven
E is mdpt ofSegs AD, BC
Given
HL
Rt. <s Thm
Def. of mdpt
Def. Rt Δs
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Statement Reason
Given:
Prove:
p.258: 22
A B
E
CD
Given
Given
AAS
Vert. <s Thm
Alt. Int. <s Thm
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Statement Reason
p. 258: 23
Given:
Prove: K
J
L
M
AAS
Given
GivenRt.<s Thm
Def. of Perpendicular
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Statement Reason
p.259q4Given:
Prove:
A C
D
E
B
F G
ASA
Given
Given
≅ Supp Thm
Def. of Supp <s
<BAC is supp of <FAB;<DEC is suppof <GED
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Statement Reason
Given:
Prove:E
FG
D
Use CPCTC
Given
Given
Alt. Int. <s Thm
Reflex. Prop of ≅
SAS
CPCTC
Converse of Alt. Int. <s Thm
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Statement Reason
Given:
Prove:
p.261ex3b
Use CPCTC
N O
PM
Given
AAS
CPCTC
Alt. Int. <s Thm.
Reflex. Prop ≅
Conv. Alt. Int. <s Thm
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Statement Reason
Given:
Prove:
Use CPCTC
A
B
C
D
Given
SSS
CPCTC
Def. of < Bisector
Reflex. Prop of ≅
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Statement Reason
Given: M is the midpoint of
Prove:
Given
SAS
CPCTC
Vert <s Thm
Def. of mdpt
M
P
QR
S
Use CPCTC
p.263: 8
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Statement Reason
p.263: 9Given:
Prove:
Use CPCTC
W X
YZ
Given
SSSCPCTC
Reflex. Prop ≅
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Statement Reason
p.263: 10
Given:
Prove:
G is the midpoint of
G is the midpoint of
Given
Def. of mdpt Def. of ≅
Through any 2 pointsthere is exactly 1 line
Reflex. Prop of ≅
Given
SSS
CPCTC
≅ Supp. Thm
FG = HG
Draw
Use CPCTC
1 2
E
F G H
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Statement Reason
p.263: 11Given:
Prove: M is the midpoint of
Given
Def. of < bisector Given
Reflex. Prop of ≅ SAS
CPCTC
Def. of mdpt
M is the midpoint of
L
MKJ
Use CPCTC
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Statement Reason
Given: ΔQRS is adjacent to ΔQTS.
Prove:
ΔQRS is adjacent to ΔQTS.
Given
Def. of < bisect Reflex. Prop of ≅
AAS CPCTC
Def. of bisect
p.263:14
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Statement Reason
Given: with E the midpoint of
Prove:
p.263: 15
Given
Def. of mdpt
Vert <s Thm
SAS
CPCTC
Conv. of Alt. Int. <s Thm
E is the mdpt. of
Use CPCTC
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Given: PS = RQ, m<1 = m<4
Prove: m<3 = m<2
Given
Def. of Perpendicular
Def. of rt triangle
Given
Def. of ≅
Reflex. Prop of ≅
SAS
CPCTC
Def of ≅
PS = RQ
m<1 = m<4
m<3 = m <2
p.264:19
1
2
P
SR
Q3
4
Use CPCTC
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