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17. Given:
/
F
>
/
J
,
/
E
>
/
H
E
w
C
w
>
G
w
H
w
Prove:
E
w
F
w
>
H
w
J
w
Proof:
We are given that
/
F
>
/
J
,
/
E
>
/
H
,
and
E
w
C
w
>
G
w
H
w
.By the Reflexive Property,
C
w
G
w
>
C
w
G
w
.Segment addition results in
EG
5
EC
1
CG
and
CH
5
CG
1
GH
.By the definition
of congruence,
EC
5
GH
and
CG
5
CG
.Substitute
to find
EG
5
CH
.By AAS,
n
EFG
>
n
HJC
.By
CPCTC,
E
w
F
w
>
H
w
J
w
.
18. Given:
T
w
X
w
i
S
w
Y
w
/
TXY
>
/
TSY
Prove:
n
TSY
>
n
YXT
Proof:
Since
T
w
X
w
i
S
w
Y
w
,
/
YTX
>
/
TYS
by
Alternate Interior Angles Theorem.
T
w
Y
w
>
T
w
Y
w
by
the Reflexive Property. Given
/
TXY
>
/
TSY
,
n
TSY
>
n
YXT
by AAS.
19. Given:
/
MYT
>
/
NYT
/
MTY
>
/
NTY
Prove:
n
RYM
>
n
RYN
Proof:
20. Given:
n
BMI
>
n
KMT
I
w
P
w
>
P
w
T
w
Prove:
n
IPK
>
n
TPB
Proof:
21. Explore:
We are given the measurement of one
side of each triangle. We need to determine
whether two triangles are congruent.
Plan:
C
w
D
w
>
G
w
H
w
, because the segments have the
same measure.
/
CFD
>
/
HFG
because vertical
angles are congruent. Since
F
is the midpoint of
D
w
G
w
,
D
w
F
w
>
F
w
G
w
.
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.
 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Angles

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