1. 4-3 Congruent Triangles Congruent triangles
Triangles that are the same size and shape
All of the vertices correspond/ “match up”
The sides of the triangles also correspond
All the parts that match are called corresponding parts.
Angles
A  F
B  D
C  E
Segments
AB  FD
BC  DE
AC  FE
If two triangles are congruent, the vertices correspond in the same order as the letters naming the triangles. A B C F D E
ABC  FDE

2. Definition of Congruent Triangles
If the corresponding parts of two triangles are congruent, then the two triangles are congruent.
If two triangles are congruent, then the corresponding parts of the two triangles are congruent.
Abbreviation:
CPCTC
Corresponding
Parts of
Congruent
Triangles are

3. Example #1
If BIG  CAT, name the congruent angles and sides. Then draw the triangles, using the arcs and slash marks to show congruent angles and sides.
Label your first triangle with the first set of letters.
Starting in the same spot on the other triangle, name it using the second set of letters.
Then figure out the corresponding parts.
Then draw your markings.
Angles
B  C
I  A
G  T
Segments
BI  CA
IG  AT
BG  CT I A T B G C

4. Check Your Progress 1A & 1B
The measures of the sides of triangles PDQ and OEC are PD = 5, DQ = 7, PQ = 11, EC = 7, OC = 5, and OE = 11
1A: Name the corresponding congruent angles and sides
1B: Name the congruent triangles

5. Theorem 4.4 Properties of Triangle Congruence
Congruence of triangles is reflexive, symmetric, and transitive

6. Example #2 Write down one triangle. HAT
Figure out what angle corresponds to the order you used.
H  B
A  O
T  Y
So HAT  BOY
The corresponding parts of two congruent triangles are marked on the figure. Write a congruence statement for the two triangles.
A congruence statement says ???  !!! A B Y H T O

7. Transformations
Congruence Transformations: The shapes maintain their congruence throughout each transformation.
Rotation (turn)
Reflection (flip)
Transition (slide)

8. Take a look at Example #2 p. 219
Now do Check your Progress 2A & 2B p. 220
Answers
2A: LM = MN = LN = 4,
L’M’ = M’N’ = L’N’ = 4