Download Ch 5-2 Congruent Triangle Proofs

Geometry
St. Barnabas HS
Bronx, NY
Geometry Lesson: Proving Segments and
Angles of Triangles Congruent
1
How do we prove corresponding segments and
angles of triangles congruent?
Do Now:
B
C
A
D
E
1) Which postulate can be used to prove ABE  DCE ?
Ans: S.A.S. Postulate
2) State 3 pairs of congruent sides.
Ans: AB  DC , BE  CE , EA  ED
3) State 3 pairs of congruent angles.
Ans: A  E , B  C , BEA  CED
2
From the definition of congruent triangles:
Corresponding Parts of Congruent Triangles are Congruent.
B
Ex: Given: ADB  CDB, BD bisects ABC
Prove: A  C , AB  CB
Statements
A
D
C
Reasons
1) ADB  CDB
2) BD bisects ABC
1) Given
2) Given
3) ABD  CBD
4) BD  BD
3) Def. angle bisector
4) Reflexive Postulate
5)
ABD  CBD
6) A  C
5) A.S.A. Postulate
6) C.P.C.T.C.
7) AB  CB
7) C.P.C.T.C.
3
T
L
1) Given: TN  LX , TL  NX
Prove: T  X
N
X
Z
2) Given: RZQ  VZQ
ZQ is an altitude of RZV
Prove: RZ  VZ
3) Given: FT  NQ, 1  3
ST  DT , FT bisects NQ
Prove: S  D, SN  DQ
R
S
N
V
Q
F
13
2 4
T
D
Q
4
D
4) Given: DR  DN , RT  NT
Prove: DT bisects RDN
T
R
D
5) Given: BDR  EZR
EB bisects DZ
Prove: DZ bisects EB
6) Given: QNB, SQ  TQ
SQN  TQN
Prove: SNB  TNB
N
B
R
E
Z
S
Q
N
B
T
Geometry Lesson: Proving Segments and
Angles of Triangles Congruent
5
3) Given: FT  NQ, 1  3
ST  DT , FT bisects NQ
Prove: S  D, SN  DQ
D
13
2 4
T
N
Statements
1) FT  NQ , 1  3
2) FTN , FTQ are rt. 's
F
S
Q
Reasons
1) Given
2) Def. Perpendicular
3) 1 compl. 2, 3 compl. 4 3)
If union of adj. 's is a rt. ,
the 's are complementary.
4) 2  4
4) Compls. of  's are  .
5) ST  DT , FT bisects NQ
6) NT  TQ
5) Given
7) STN  DTQ
8) S  D, SN  DQ
6) Def. line bisector
7) S.A.S. Postulate
8) C.P.C.T.C
Geometry Lesson: Proving Segments and
Angles of Triangles Congruent
6
D
4) Given: DR  DN , RT  NT
Prove: DT bisects RDN
T
R
Statements
N
Reasons
1) DR  DN , RT  NT
2) DT  DT
1) Given
2) Reflexive postulate
RDT  NDT
4) RDT  NDT
5) DT bisects RDN
3) S.S.S. postulate
3)
4) C.P.C.T.C.
5) Def. angle bisector
7