17. Given:
F
J
,
E
H
EC
GH
Prove:
EF
HJ
Proof:
We are given that
F
J
,
E
H
,
and
EC
GH
. By the Reflexive Property,
CG
CG
. Segment addition results in
EG
EC
CG
and
CH
CG
GH
. By the definition
of congruence,
EC
GH
and
CG
CG
. Substitute
to find
EG
CH
. By AAS,
EFG
HJC
. By
CPCTC,
EF
HJ
.
18. Given:
TX
SY
TXY
TSY
Prove:
TSY
YXT
Proof:
Since
TX
SY
,
YTX
TYS
by
Alternate Interior Angles Theorem.
TY
TY
by
the Reflexive Property. Given
TXY
TSY
,
TSY
YXT
by AAS.
19. Given:
MYT
NYT
MTY
NTY
Prove:
RYM
RYN
Proof:
20. Given:
BMI
KMT
IP
PT
Prove:
IPK
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:
CD
GH
, because the segments have the
same measure.
CFD
HFG
because vertical
angles are congruent. Since
F
is the midpoint of
DG
,
DF
FG
.
Solve:
We are given information about sideside
angle (SSA). This is not a method to prove two
triangles congruent.
Examine:
Use a compass, protractor, and ruler to
draw a triangle with the given measurements. For
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Angles, Trigraph, NYT, linear pair, Reflexive Property

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