5.3: One Step Congruence Proofs
Brinkman
SKILLS TO AQUIRE
 Make and justify conclusions about congruent figures.
REVIEW: Draw two triangles ABC and A’B’C’ that are congruent. Label ALL the congruencies! 
REVIEW: JUSTIFICATIONS THAT SEGMENTS ARE CONGRUENT!
1.) If the perpendicular bisector of AB
intersects AB at M, then AM  MB.

A

M
Definition of Perpendicular Bisector
B

2.) If M is the midpoint of AB, then
AM  MB.

A
 M
Definition of Midpoint
B
3.) Corresponding parts of congruent
figures are congruent.
B’
B
A’
C’
A
CPCF Theorem
C
4.) If AB = CD, then AB  CD.
Segment Congruence Theorem

5.) If A and B are on circle O, then AO BO.
Definition of Circle
6.) If one segment is the image of another

under an isometry, then
the segments
are congruent.
Definition of Congruence
REVIEW: JUSTIFICATIONS THAT ANGLES ARE CONGRUENT!
1.) If two parallel lines are cut by a
transversal then corresponding
angles are congruent.
Corresponding Angles Postulate
1
2
2.) If BD is the bisector of ABC ,
then ABD  DBC .

B

Definition of Angle Bisector
A
D

C
3.) Corresponding parts of congruent
figures are congruent.
CPCF Theorem
4.) If m1  m2 , then 1  2 .
Angle Congruence Theorem
 5.) If 1 and 2
 are vertical angles,
then 1  2 .


6.) If one angle is the image of another

under an isometry, then the angles
are congruent.
Vertical Angles Theorem
Definition of Congruence
Example: In the diagram points X, Y and Z are on circle O, O is the center point and OY is a
perpendicular bisector of XZ.
X
Provide the justification for each conclusion:

A.) ZP  PZ ______________________________

O
P
B.) OX  OZ ______________________________




C.) OP  OP ______________________________
D.) ZPO  YPX __________________________
Z
Y