Geometry
HS Mathematics
Unit: 04 Lesson: 02
Proving Triangles Congruent and CPCTC - NOTES
The definition of congruent triangles states two triangles are congruent if and only if their
corresponding parts are congruent. If and only if is used when both the conditional and its converse
are true. Therefore the converse is true:
Corresponding parts of congruent triangles are congruent. (CPCTC)
This can be used to prove parts of triangles congruent by first proving the triangles congruent.
Examples: Justify the following using two column or flow proofs.
2. Prove: EG  JI
1. Prove: D  B
A
K
I
E
J
D
C
B
G
F
Teacher Notes:
1. Show triangles congruent by SSS and D  B by CPCTC.
2. Show triangles congruent by AAS or HA and EG  JI by CPCTC.
©2012, TESCCC
07/23/12
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Geometry
HS Mathematics
Unit: 04 Lesson: 02
Proving Triangles Congruent and CPCTC - HOMEWORK
Practice Problems
1. Given: LMN is an isosceles triangle with vertex M.
MP bisects LN .
Prove: LMP  NMP
Statements
Reasons
LMN is an isosceles
triangle with vertex M.
MP bisects LN .
LM  NM
LP  NP
MP  MP
LMP  NMP
LMP  NMP
©2012, TESCCC
L
N
P
A
2. Given: AB  BC , CD  BC
A  D
Prove: AC  DB
Statements
AB  BC , CD  BC
A  D
ABC and DCB are
right angles.
BC  BC
ABC  DCB
AC  DB
M
Reasons
B
C
07/23/12
D
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Geometry
HS Mathematics
Unit: 04 Lesson: 02
Proving Triangles Congruent and CPCTC
3. Given: C is the midpoint
of AD and BE

Prove: A  D
Statements
C is the midpoint of
AD and BE
BC  EC
AC  DC
ACB  DCE
ABC  DEC
A  D
4. Given: BC AD , AB
Prove: AD  CB
Statements
B
Reasons
C
A
E
CD
B
C
Reasons
BC AD , AB P CD
BAC  DCA
BCA  DAC
AC  AC
ABC  CDA
AD  CB
©2012, TESCCC
D
A
07/23/12
D
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