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Lesson: 4.3 Exploring CONGRUENT Triangles
Pages: 196 – 197
Objectives:
 To NAME and LABEL Corresponding PARTS
of CONGRUENT Triangles
 To STATE the CPCTC Theorem
• congruent triangles
• congruence transformations
GEOMETRY 4.3
Congruent Polygons have the:

SAME Size

SAME Shape
GEOMETRY 4.3
Congruent Polygons have the:

SAME Size

SAME Shape
Congruent TRIANGLES have

Congruent CORRESPONDING SIDES

Congruent CORRESPONDING Angles
GEOMETRY 4.3
Congruent TRIANGLES have

Congruent CORRESPONDING SIDES

Congruent CORRESPONDING Angles
F
C
A
B
D
E
GEOMETRY 4.3
Congruent TRIANGLES have

Congruent CORRESPONDING SIDES

Congruent CORRESPONDING Angles
E
C
A
B
D
F
GEOMETRY 4.3
Congruent TRIANGLES have

Congruent CORRESPONDING SIDES

Congruent CORRESPONDING Angles
Because CORRESPONDING parts determine Congruence:
You may have to:
 Slide
 Rotate, or
 Flip
Figures to determine
whether they are CONGRUENT
GEOMETRY 4.3
Congruent TRIANGLES have

Congruent CORRESPONDING SIDES

Congruent CORRESPONDING Angles
The way you NAME the Triangle establishes the
CORRESPONDENCE:
GEOMETRY 4.3
To WRITE the CORRESPONDING
Parts of Congruent Triangles,
use
GEOMETRY 4.3
SO, if
ABC 
Congruent Angles
FGH:
Congruent Sides
GEOMETRY 4.3
SO, if
ABC 
Congruent Angles
FGH:
Congruent Sides
Be sure to WRITE the LETTERS of VERTICES
in the CORRECT ORDER when you write a  Statement.
GEOMETRY 4.3
A THEOREM:
Two Triangles are CONGRUENT
if and only if
Their CORRESPONDING PARTS are CONGRUENT
GEOMETRY 4.3
A THEOREM:
Two Triangles are CONGRUENT
if and only if
Their CORRESPONDING PARTS are CONGRUENT
This is called
CPCTC
GEOMETRY 4.3
A THEOREM:
Two Triangles are CONGRUENT
if and only if
Their CORRESPONDING PARTS are CONGRUENT
This is called
CPCTC
(Corresponding Parts of Congruent Triangles are Congruent.)
GEOMETRY 4.3
TRU 
TSU

Name the CORRESPONDING CONGRUENT Angles & Sides.
GEOMETRY 4.3
A THEOREM:
CONGRUENCE of TRIANGLES is:

REFLEXIVE

SYMMETRIC, and

TRANSITIVE
GEOMETRY 4.3
A THEOREM:
CONGRUENCE of TRIANGLES is:

REFLEXIVE

SYMMETRIC, and

TRANSITIVE
GEOMETRY 4.3
GEOMETRY 4.3
GEOMETRY 4.3
GEOMETRY 4.3
GEOMETRY 4.3
GEOMETRY 4.3
GEOMETRY 4.3
B. COORDINATE GEOMETRY
The vertices of ΔRST are R(–3,
0), S(0, 5), and T(1, 1). The
vertices of ΔRST are R(3, 0),
S(0, –5), and T(–1, –1). Use the
Distance Formula to verify that
corresponding sides are
congruent. Name the
congruence transformation for
ΔRST and ΔRST.
GEOMETRY 4.3
You should be able to:
 State the CPCTC Theorem
 DESCRIBE how Triangle Congruence is
Reflexive, Symmetric and Transitive
 Use CPCTC in a Proof
 DETERMINE if Corresponding Part of
Triangles are Congruent.
GEOMETRY 4.4
Recall that CONGRUENCE means
o Same SHAPE
o Same SIZE
GEOMETRY 4.4
Recall that CONGRUENCE means
o Same SHAPE
o Same SIZE
Now for some SHORTCUT postulates and theorems
that don’t require proving ALL Corresponding Angles
and ALL Corresponding Sides are Congruent.
GEOMETRY 4.4
SSS Postulate
If the SIDES of one triangle are CONGRUENT
to the SIDES of a Second Triangle,
THEN
the Triangles are CONGRUENT.
GEOMETRY 4.4
DEFINITION:
The Included Angle of Two Sides is the Angle
formed by them.
C
2
1
A
3
B
GEOMETRY 4.4
SAS Postulate
If TWO SIDES and the INCLUDED ANGLE of one Triangle
are CONGRUENT to
TWO SIDES and the INCLUDED ANGLE of another Triangle
THEN
The Triangles are CONGRUENT.
GEOMETRY 4.4
GEOMETRY 4.4
GEOMETRY 4.4
Which pair of Triangles are CONGRUENT?
GEOMETRY 4.4
Which pair of Triangles are CONGRUENT?
GEOMETRY 4.4
Which pair of Triangles are CONGRUENT?
GEOMETRY 4.4
Which pair of Triangles are CONGRUENT?
GEOMETRY 4.4
GEOMETRY 4.4