CONGRUENT TRIANGLES

1. TRIANGLE
CONGRUENCE
POSTULATES

2. At the end of the lesson, students should be able to
inspect the corresponding parts of the triangles and
identify its congruence using the four postulates
(SSS, SAS, ASA, AAS) .
Preliminary activities such as triangle construction
and review on topics about similar triangles can be
conducted before the lesson proper.
About the material
You can include in the
presentation notes or
additional examples as
needed.

3. WHAT YOU'LL
LEARN TODAY
• SSS Postulate
• SAS Postulate
• ASA Postulate
• AAS Postulate

4. "Triangle ABC is congruent to Triangle DEF"
A
B C
D
E F
△ABC ≅ △DEF
Two or more triangles are congruent if they have the same size and shape.
Congruence is denoted by the symbol "≅" and read as "is congruent to"
What are congruent triangles?

5. Examples
Congruent triangles can be flipped, rotated and mirrored and will still be congruent.
Not Congruent Triangles
Congruent Triangles

6. corresponding sides
Included Angle
The angle between
two sides of a triangle.
WORD BANK
Included Side
The side between two
angles of a triangle
Corresponding Parts
Pairs of sides or angles of two
triangles that are on same position.
Let's look at important terms that will
be used in the lesson.
corresponding angles
included
side
included
angle

7. ASA
(angle-side-angle)
SSS
(side-side-side)
SAS
(side-angle-side)
AAS
(angle-angle-side)
Postulates are statements which are accepted as true without proof.
The following postulates are used to verify congruence of two triangles.
Triangle Congruence Postulates

8. △GHI ≅ △JKL
If the three sides of the first triangle is congruent to its corresponding
sides on the second triangle, then the two triangles are congruent.
Short lines (hatches) are used to mark congruent sides.
SSS Postulate
G
H I
J
K L

9. If two sides and the included angle of the first triangle are congruent to
two sides and the included angle of the second triangle, then the
triangles are congruent. Arcs are used to mark congruent angles.
SAS Postulate
M
△MNO ≅ △PQR
N O
P
Q R
included
angle
side
side

10. If two angles and the included side of the first triangle are congruent to
two angles and the included side of the second triangle, then the
triangles are congruent.
ASA Postulate
S
T U
V
W X
included side
angle angle
△STU ≅ △VWX

11. If two angles and the non-included side of the first triangle are
congruent to two angles and the non-included side of the second
triangle, then the triangles are congruent.
AAS Postulate
A D
△ABC ≅ △DEF
B E
C F
non-included
side
non-included
side
angle angle
angle angle

12. A
B C
D
E F
X Y
Z
T
U V
G
H
J
R
S
K
L M
O
P Q
CHECK YOUR
UNDERSTANDING
Which of the following pairs of triangles are congruent?

13. A
B C
D
E F
X Y
Z
T
U V
G
H
J
R
S
K
L M
O
P Q
CHECK YOUR
UNDERSTANDING
congruent by
ASA
no postulate
can determine
the congruence
no postulate can
determine the
congruence
congruent
by AAS
Answers:

14. CHECK YOUR
UNDERSTANDING
A
B
C D
E
F
G
H
J
K
L
M
N
O P
Q
R S
T
U V
W
Which of the following pairs of triangles are congruent?
A

15. CHECK YOUR
UNDERSTANDING
congruent
by SAS
congruent
by AAS
no postulate can
determine the
congruence
congruent
by SSS
Answers:
A
B
C D
E
F
G
H
J
K
L
M
N
O P
Q
R S
T
U V
W

16. THANK YOU!
Let's make our next discussion more lively by doing
advanced reading about Two-Column Proofs.

17. RESOURCE
PAGE
Use these icons and illustrations
in your Canva Presentation.
Happy designing! Don't forget
to delete this page before
presenting.