Congruent Triangles * Overlapping Triangles

```Congruent Triangles –
Overlapping Triangles
Pg. 12
Pg. 12 #1
Statement
Reason
1. DC  BA
1. Given
2. DF  BE
2. Given
3. CE  AF
3. Given
4. FE  FE
4. Reflexive Postulate
5. CE  FE  AF  FE
6. CE  FE  CF
AF  FE  AE
6. Partition Postulate
7. CF  AE
7. Substitution Postulate
8. ΔAEB  ΔCFD
8. SSS  SSS
Pg. 12 #2
Statement
Reason
1. CE  DF
2. 1  2
1. Given
3. AE  BF
3. Given
4. EF  EF
4. Reflexive Postulate
5. AE  EF  BF  EF
6. AE  EF  AF
BF  EF  BE
6. Partition Postulate
7. AF  EB
7. Substitution Postulate
8. ΔAFD  ΔBEC
8. SAS  SAS
2. Given
Pg. 12 #3
Statement
Reason
1. SX  SY
1. Given
2. XR  YT
2. Given
3. S  S
3. Reflexive Postulate
4. SX  XR  SY  YT
5. SX  XR  SR
SY  YT  ST
5. Partition Postulate
6. SR  ST
6. Substitution Postulate
7. ΔRSY  ΔTSX
7. SAS  SAS
Pg. 12 #4
Statement
Reason
1. DA  CB
1. Given
2. DA  AB
2. Given
3. CB  AB
3. Given
4. DAB and CBA
are right angles
4. Perpendicular segments
form right angles
5. DAB  CBA
5. All right angles are congruent
6. AB  AB
6. Reflexive Postulate
7. ΔDAB  ΔCBA
7. SAS  SAS
Pg. 12 #7
Statement
Reason
1. LP  PN
1. Given
2. MN  PN
2. Given
3. LP  MN
3. Given
4. PR  NS
4. Given
5. 1 and 2 are right angles
5. Perpendicular segments
form right angles
6. 1  2
6. All right angles are congruent
7. RS  RS
7. Reflexive Postulate
8. PR  RS  NS  RS
9. PR  RS  PS
NS  RS  NR
9. Partition Postulate
10. PS  NR
10. Substitution Postulate
11. ΔLPS  ΔMNR
11. SAS  SAS
Pg. 12 #6
Statement
Reason
1. AB  BF
1. Given
2. CD  BF
2. Given
3. BD  FE
3. Given
4. 1  2
4. Given
5. ABD and CDF
are right angles
5. Perpendicular segments
form right angles
6. ABD  CDF
6. All right angles are congruent
7. DE  DE
7. Reflexive Postulate
8. BD  DE  FE  DE
9. BD  DE  BE
FE  DE  FD
9. Partition Postulate
10. BE  FD
10. Substitution Postulate
11. ΔABE  ΔCDF
11. ASA  ASA
Pg. 12 #9
Statement
Reason
1. TR  TS
1. Given
2. MR  NS
3. T  T
2. Given
3. Reflexive Postulate
4. TR  MR  TS  NS
4. Subtraction Postulate
5. TR  MR  TM
TS  NS  TN
5. Partition Postulate
6. TM  TN
6. Substitution Postulate
7. ΔRTN  ΔSTM
7. SAS  SAS
Pg. 13 #10
Statement
Reason
1. AB  DB
1. Given
2. A  D
2. Given
3. DBA  CBE
3. Given
4. 1  1
4. Reflexive Postulate
5. DBA  1  CBE  1
6. DBA 1  ABE
CBE  1  CBD
6. Partition Postulate
7. ABE  CBD
7. Substitution Postulate
8. ΔABE  ΔDBC
8. ASA  ASA
Pg. 13 #11
Statement
Reason
1. DA  EC
1. Given
2. DC  EA
3. AC  AC
2. Given
3. Reflexive Postulate
4. CAD  ACE
4. SSS  SSS
5. DCA  EAC
5. CPCTC
Pg. 13 #12
Statement
Reason
1. DA  AB
1. Given
2. CB  AB
2. Given
3. AD  BC
3. Given
4. DAB and CBA
are right angles
4. Perpendicular segments
form right angles
5. DAB  CBA
5. All right angles are congruent
6. AB  AB
6. Reflexive Postulate
7. ΔDAB  ΔCBA
7. SAS  SAS
8. AC  BD
8. CPCTC
Pg. 12 #13
Statement
Reason
1. BD  BE
1. Given
2. DA  EC
2. Given
3. BD  DA  BE  EC
4. BD  DA  BA
BE  EC  BC
4. Partition Postulate
5. BA  BC
5. Substitution Postulate
6. B  B
6. Reflexive Postulate
7. DBC  EBA
7. SAS  SAS
8 .  A  C
8. CPCTC
Pg. 13 #14
Statement
Reason
1. AC  BC
1. Given
2. CE  CD
2. Given
3. AE  BD
3. Given
4. ΔACE  ΔBCD
4. SSS  SSS
5. ACE  BCD
5. CPCTC
6. 3  3
7. ACE  3  BCD  3
6. Reflexive Postulate
8. ACE  3  1
BCD  3  2
9. 1  2
8. Partition Postulate
7. Subtraction Postulate
9. Substitution Postulate
Pg. 13 #16
Statement
Reason
1. CF  FD
1. Given
2. CE  FB
3. ECF  CFA
2. Given
4. CFA  BFD
4. Vertical angles are
congruent
5. ECF  BFD
5. Substitution Postulate
6. ΔCFE  ΔFDB
6. SAS  SAS
7. EF  BD
7. CPCTC
3. Given
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