Download Notes Section 4-4

Geometry
Notes Section 4-4
What you’ll learn. . . .
How to use the SSS Postulate to
test for triangle congruence
 How to use the SAS Postulate to
test for triangle congruence

Vocabulary

Included angle
Remember the Definition of Congruent
Triangles

Two triangles are congruent if and only
if their corresponding parts are
congruent.

According to this definition we would
have to show all six pairs of
corresponding parts congruent to prove
two triangles are congruent.

There has to be a shorter way. . .

What is the minimum number of
corresponding congruent parts
necessary to show to triangles are
congruent?
 Would
knowing
all three pairs of
sides congruent
be enough?
 This
is called
the Side-SideSide (or SSS)
Postulate

Side-Side-Side Postulate: If the
sides of one triangle are congruent
to the sides of a second triangle,
then the triangles are congruent.

You can prove two triangles are
congruent by showing they
have sides of the same length.
Example #1: Identify the
congruent triangles in each figure.
Example #2: Determine whether
ΔDEF  ΔPQR given the coordinates
of the vertices. Explain.
D(-6, 1), E(1, 2), F(-1, -4), P(0, 5), Q(7, 6), R(5, 0)
You can show all 3 pairs of corresponding sides
are congruent by using the distance formula.
DE  ( 6  1)  (1  2)  50
2
2
EF  (1  ( 1))  ( 2  ( 4 ))  40
2
2
DF  ( 6  ( 1))  (1  ( 4 ))  50
2
2
Example #2 (continued): Now for PQ,
QR, and PR
D(-6, 1), E(1, 2), F(-1, -4), P(0, 5), Q(7, 6), R(5, 0)
PQ  ( 0  7)  ( 5  6 )  50
2
2
QR  ( 7  ( 5 ))  ( 6  0 )  40
2
2
PR  ( 0  5 )  ( 5  0 )  50
2
2
Since DE  PQ , EF  QR ,
and DF  PR , DEF  PQR by SSS.
Example 3:
.
Example #4:
Example #5: Write a twocolumn proof.

Might there be another shortcut
combination of parts? Possibly
mixing pairs of congruent sides
with pairs of congruent angles?
 Would
knowing
all two pairs of
sides congruent
and the angles
between them
be enough?
 This
is called
the SideAngle-Side
(or SAS)
Postulate

Side-Angle-Side Postulate: If the
two sides and the included angle
of one triangle are congruent to
two sides and the included angle
of another triangle, then the two
triangles are congruent.

You can prove two triangles are
congruent by showing they
have 2 sides and their included
angles equal.
Example #6: Identify the
congruent triangles in each figure.
Example #7: For each diagram,
determine which pairs of triangles
can be proved congruent by the
SAS Postulate.
Example #8: For each diagram,
determine which pairs of triangles
can be proved congruent by the
SAS Postulate.
Example #9: For each diagram,
determine which pairs of triangles
can be proved congruent by the
SAS Postulate.
Example #10: Write a twocolumn proof
Have you learned. . . .
How to use the SSS Postulate to
test for triangle congruence
 How to use the SAS Postulate to
test for triangle congruence


Assignment:


Non-Proof: Worksheet 4-4
Proof: p.204(10-24Even, 30-47)