Transcript CPCTC - Camden Central School

CPCTC
Congruent Triangles
Pg. 3 #1
Statement
Reason
1. LN bisectsKLM
1. Given
2. LKM  LMK
2. Given
3. 1  2
3. An angle bisector divides an
angle into two congruent parts
4. LN  LN
4. Reflexive postulate
5. ΔLKN  ΔLMN
5. AAS  AAS
6. NM  NK
6. CPCTC
Pg. 3 #2
Statement
Reason
1. MN  MP
1. Given
2. MR bisects NP
2. Given
3. NQ  QP
3. A segment bisector divides a
segment into two congruent parts
4. MQ  MQ
4. Reflexive postulate
5. ΔMQN  ΔMQP
5. SSS  SSS
6. NQM  PQM
6. CPCTC
Pg. 3 #3
Statement
Reason
1. HA  MT
1. Given
2. HMA  HTA
2. Given
3. 1 and 2 are
right angles
3. Perpendicular segments form
right angles
4. 1  2
4. All right angles are congruent
5. AH  AH
5. Reflexive postulate
6. ΔMAH  ΔTAH
6. AAS  AAS
Pg. 3 #4
Statement
Reason
1. 1  2
1. Given
2. SM  RT
2. Given
3. Two adjacent angles that form a
3. 1 and 3 are linear pairs
2 and 4 are linear pairs
straight line are a linear pair
4. 1 and 3 are supplementary 4. Linear pairs are supplementary
2 and 4 are supplementary
5. 3  4
5. Supplements of congruent
angles are congruent
6. SR  ST
6. Sides opposite congruent
angles of a triangle are congruent
Pg. 3 #5
Statement
Reason
1. AB  BD
1. Given
2. ED  DB
2. Given
3. AE bisects BD
3. Given
4. B and D are
right angles
4. Perpendicular segments form
right angles
5. B  D
5. All right angles are congruent
6. BC  CD
6. A segment bisector
divides a segment into 2
congruent parts
7. 1  2
7. Vertical angles are congruent
8. ΔABC  ΔEDC
8. ASA  ASA
9. AB  ED
9. CPCTC
Pg. 3 #6
Statement
Reason
1. MH  AT
1. Given
2. 1  2
2. Given
3. Two adjacent angles that form a
3. 1 and 3 are linear pairs
2 and 4 are linear pairs
straight line are a linear pair
4. 1 and 3 are supplementary 4. Linear pairs are supplementary
2 and 4 are supplementary
5. 3  4
5. Supplements of congruent
angles are congruent
6. MT  MT
6. Reflexive postulate
7. ΔMAT  ΔTHM
7. SAS  SAS
Pg. 3 #7
Statement
Reason
1. MR  MP
1. Given
2. QM bisectsPMR
2. Given
3. 1  2
3. An angle bisector divides an
angle into two congruent parts
4. MQ  MQ
4. Reflexive postulate
5. ΔMQP  ΔMQR
5. SAS  SAS
6. PQ  RQ
6. CPCTC
Pg. 3 #8
Statement
Reason
1. ML  AW
1. Given
2. KT  MA
2. Given
3. 1  2
3. Given
4. TM  TM
4. Reflexive postulate
5. KT  TM  MA  TM
5. Addition postulate
6. KT  TM  KM
MA  TM  AT
6. Partition postulate
7. KM  AT
7. Substitution postulate
8. KML  TAW
8. SAS  SAS
9. KL  TW
9. CPCTC
Pg. 4 #9
Statement
Reason
1. MI  TG
1. Given
2. ME  RG
2. Given
3. MI  ME
3. Given
4. 1 and 2
are right angles
4. Perpendicular lines form
right angles
5. ΔMIG and ΔMEG
are right triangles
5. Triangles with right angles
are right triangles
6. MG  MG
7. ΔMIG  ΔMEG
8. TGP  RGP
6. Reflexive Postulate
7. Hy - leg  Hy - leg
8. CPCTC
Pg. 4 #10
Statement
Reason
1. DO  OA
1. Given
2. TA  OA
2. Given
3. DO  TA
3. Given
4. OC  AG
4. Given
5. 1 and 2
are right angles
5. Perpendicular lines form
right angles
6. 1  2
6. All right angles are congruent
7. GC  GC
7. Reflexive Postulate
8. OC  CG  AG  GC
8. Subtraction Postulate
9. OC  CG  OG
AG  GC  AC
9. Partition Postulate
10. OG  AC
10. Substitution Postulate
11. ΔDOG  ΔTAC
11. SAS  SAS
12. DG  TC
12. CPCTC
Pg. 4 #12
Statement
Reason
1. CT  CH
1. Given
2. CX bisectsTCH
2. Given
3. 1  2
3. An angle bisector divides an
angle into two congruent parts
4. CX  CX
4. Reflexive postulate
5. ΔCXT  ΔCXH
5. SAS  SAS
6. TX  XH
7. HTX  THX
6. CPCTC
7. Angles opposite congruent
sides of a triangle are
congruent.