Two triangles are congruent if and only if their
corresponding parts are congruent. (CPCTC)

The seat and legs of this stool form two triangles. Suppose the
measures in inches
QR
=12,
RS
=23,
QS
=24,
RT
=12,
TV
=24,
and
RV
=23.
A)
Name the corresponding congruent angles and sides.
B)
Name the congruent triangles.

Show that the polygons are congruent by
identifying all the congruent corresponding parts.
Then write a congruence statement.

In the diagram,
. Find the values of x
and y.
DFE
ABC

Theorem 4.3
–
Third Angles Theorem
–
If two
angles of one triangle are congruent to two angles
of a second triangle, then the third angles of the
triangles are congruent.

The planners of the Senior Banquet decide to fold
the dinner napkins using the Triangle Pocket Fold
so that they can place a small gift in the pocket. If
.
,
40
,
SRT
m
find
NPQ
m
and
RST
NPQ

Write a two-column proof.
Given:
Prove:
GFE
DFE
G
D
GF
DF
GE
DE
,
,
,
GEF
DEF

Theorem 4.4
–
Congruence of triangles is reflexive,
symmetric, and transitive.

Section 4-4
Proving Congruence
SSS, SAS

I CAN….
•
Use the SSS Postulate to test for triangle
congruence.
•
Use the SAS Postulate to test for triangle
congruence.

Postulate 4.1
–
Side-Side-Side Congruence
–
If
the sides of one triangle are congruent to the
sides of a second triangle, then the triangles
are congruent.
Abbreviation:
SSS

Write a proof.
Given:
and L is the midpoint of
Prove:
,
,
JL
HL
KJ
GH
GK
KJL
GHL
G
J
L
H
K

The tail of an orca whale can be viewed as two triangles that
share a common side. Write a two-column proof to prove that
if
and
.
CYA
BYA
AC
AB
CY
BY

Included Angle
–
In a triangle, the angle between
two given sides.
Included Angle

Postulate 4.2
–
Side-Angle-Side Congruence
–
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.
Abbreviation:
SAS

Write a two-column proof.
Given:
X
is the midpoint of
X
is the midpoint of
Prove:
BXA
DXC
BD
AC