1. Chapter 8 Proving Triangles Congruent
Section 8.1
SSS and SAS Postulates

2. ΔABC  ΔXYZ What You'll Learn
Congruent Triangles
What You'll Learn
You will learn to identify corresponding parts of congruent
triangles
If a triangle can be translated, rotated, or reflected onto another triangle, so
that all of the vertices correspond, the triangles are _________________.
congruent triangles
The parts of congruent triangles that “match” are called ______________.
congruent parts
The order of the ________ indicates the corresponding parts!
ΔABC  ΔXYZ
vertices

3. These relationships help define the congruent triangles.
In the figure, ΔABC 
ΔFDE. A
As in a mapping, the order of the _______ indicates the corresponding parts.
vertices C B
Congruent Angles
Congruent Sides
A  F
AB  FD F E D
B  D
BC  DE
C  E
AC  FE
These relationships help define the congruent triangles.

4. If the _________________ of two triangles are congruent, then
Congruent Triangles
Definition of
Congruent
Triangles
If the _________________ of two triangles are congruent, then
the two triangles are congruent.
corresponding parts
If two triangles are _________, then the corresponding parts
of the two triangles are congruent.
congruent

5. ΔRST  ΔXYZ ΔRST  ΔXYZ. Find the value of n.
Congruent Triangles
ΔRST  ΔXYZ. Find the value of n. T S R Z X Y
40°
(2n + 10)°
50°
90°
ΔRST  ΔXYZ
identify the corresponding parts
corresponding parts are congruent
S  Y
50 = 2n + 10
subtract 10 from both sides
1 - 28
40 = 2n
divide both sides by 2
20 = n

6. SSS and SAS
What You'll Learn
You will learn to use the SSS and SAS tests for congruency.

7. 4) Construct a segment congruent to CB. 5) Label the intersection F.
SSS and SAS
4) Construct a segment congruent to CB.
5) Label the intersection F.
2) Construct a segment congruent to AC. Label the endpoints of the segment D and E.
1) Draw an acute scalene triangle on a piece of paper. Label its vertices
A, B, and C, on the interior of each angle.
6) Draw DF and EF.
3) Construct a segment congruent to AB. A C B D E F
This activity suggests the following postulate.

8. Triangles are congruent. sides three corresponding
SSS and SAS
Postulate 5-1
SSS
Postulate
If three _____ of one triangle are congruent to _____ _____________ sides of another triangle, then the two
Triangles are congruent.
sides
three
corresponding A B C R S T
If AC 
RT and
AB 
RS and
BC  ST
then ΔABC
 ΔRST

9. In two triangles, ZY  FE, XY  DE, and XZ  DF.
SSS and SAS
In two triangles, ZY  FE, XY  DE, and XZ  DF.
Write a congruence statement for the two triangles. X D Z Y F E
Sample Answer:
ΔZXY  ΔFDE

10. In a triangle, the angle formed by two given sides is called the
SSS and SAS
In a triangle, the angle formed by two given sides is called the
____________ of the sides.
included angle
C is the included
angle of CA and CB A B C
A is the included
angle of AB and AC
B is the included
angle of BA and BC
Using the SSS Postulate, you can show that two triangles are congruent if their corresponding sides are congruent.
You can also show their congruence
by using two sides and the ____________.
included angle

11. If ________ and the ____________ of one triangle are
SSS and SAS
Postulate 5-2
SAS
Postulate
If ________ and the ____________ of one triangle are
congruent to the corresponding sides and included angle of
another triangle, then the triangles are congruent.
two sides
included angle A B C R S T
If AC 
RT and
A 
R and
AB  RS
then ΔABC
 ΔRST

12. Example Proof – SAS – Postulate
Given: N is the midpoint of LW N is the midpoint of SK
Prove:
N is the midpoint of LW N is the midpoint of SK
Given
Definition of Midpoint
Vertical Angles are congruent
SAS Postulate

13. NO! On a piece of paper, write your response to the following:
SSS and SAS
On a piece of paper, write your response to the following:
Determine whether the triangles are congruent by SAS.
If so, write a statement of congruence and tell why they are congruent.
If not, explain your reasoning. P R Q F E D
NO!
D is not the included angle for DF and EF.