Download 4-3 Congruent Triangles - Ms. Fowls` Math Classes

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.
B
A
ABC  FDE
C F
• Angles
– A  F
– B  D
– C  E
• Segments
– AB  FD
– BC  DE
– AC  FE
D
If two triangles
are congruent,
the vertices
correspond in the
same order as
the letters
naming the
triangles.
E
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
Congruent
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
B
A
G
C
T
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
Theorem 4.4
• Properties of Triangle Congruence
• Congruence of triangles is reflexive,
symmetric, and transitive
Example #2
• 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
H
T
• Write down one triangle.
• HAT
• Figure out what angle
•
•
•
•
corresponds to the order
you used.
HB
AO
TY
So HAT  BOY
Transformations
• Congruence Transformations: The shapes
maintain their congruence throughout
Rotation (turn)
each transformation.
Reflection (flip)
Transition (slide)
Take a look at Example #2 p. 219
• Now do Check your Progress 2A & 2B p.
220
• Answers
• 2A: LM = 2 5
L’M’ = 2 5
MN = 2 5
M’N’ = 2 5
LN = 4,
L’N’ = 4