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Lesson: Congruent Triangles
Contributed by: Pappal
There are 5 common ways to
There are 5 common ways to
prove triangles congruent:
There are 5 common ways to
prove triangles congruent:
Side-Side-Side
There are 5 common ways to
prove triangles congruent:
Side-Side-Side
Side-Angle-Side
There are 5 common ways to
prove triangles congruent:
Side-Side-Side
Side-Angle-Side
Angle-Side-Angle
There are 5 common ways to
prove triangles congruent:
Angle-Angle-Side or Side-Angle-Angle
Side-Side-Side
Side-Angle-Side
Angle-Side-Angle
There are 5 common ways to
prove triangles congruent:
Hyponetuse-Leg
Angle-Angle-Side or Side-Angle-Angle
Side-Side-Side
Side-Angle-Side
Angle-Side-Angle
There are 5 common ways to
prove triangles congruent:
Hyponetuse-Leg
Side-Angle-Angle
Side-Side-Side
Side-Angle-Side
Angle-Side-Angle
SAA
?
ASA
?
SAS
?
HL
?
SSS
?
SAA is the same as which of the following:
AAS
ASA
SAS
SSS
In SSS the triangles have 3 pairs of sides congruent
In SSS the triangles have 3 pairs of sides congruent
In SSS the triangles have 3 pairs of sides congruent
In SSS the triangles have 3 pairs of sides congruent
These two sides are equal
In SSS the triangles have 3 pairs of sides congruent
In SSS the triangles have 3 pairs of sides congruent
These two sides are equal
In SSS the triangles have 3 pairs of sides congruent
In SSS the triangles have 3 pairs of sides congruent
These two sides are equal
What side is equal to side AB?
A
C
B
D
F
E
For SAS, two sides are congruent and the angles
in between
For SAS, two sides are congruent and the angles
in between
For SAS, two sides are congruent and the angles
in between
For SAS, two sides are congruent and the angles
These two sides are equal
in between
For SAS, two sides are congruent and the angles
in between
For SAS, two sides are congruent and the angles
These two sides are equal
in between
For SAS, two sides are congruent and the angles
in between
For SAS, two sides are congruent and the angles
These angles are congruent
in between
For SAS, two sides are congruent and the angles
The angle HAS to be
in between
For SAS, two sides are congruent and the angles
The angle HAS to be
BETWEEN the sides
in between
For SAS, two sides are congruent and the angles
The angle HAS to be
BETWEEN the sides
in between
For SAS, two sides are congruent and the angles
The angle HAS to be
BETWEEN the sides
in between
For SAS, two sides are congruent and the angles
The angle HAS to be
BETWEEN the sides
This angle is
between the sides
in between
For SAS, two sides are congruent and the angles
The angle HAS to be
BETWEEN the sides
in between
For SAS, two sides are congruent and the angles
The angle HAS to be
BETWEEN the sides
These angles are
not between the sides
in between
For SAS, two sides are congruent and the angles
The angle HAS to be
BETWEEN the sides
in between
For SAS, two sides are congruent and the angles
The angle HAS to be
BETWEEN the sides
in between
For SAS, two sides are congruent and the angles
The angle HAS to be
BETWEEN the sides
This angles is
between the sides
in between
For SAS, two sides are congruent and the angles
The angle HAS to be
BETWEEN the sides
in between
For SAS, two sides are congruent and the angles
The angle HAS to be
BETWEEN the sides
These angles are not
between the sides
in between
Which angle is between the sides?
B
C
∡A
∡B
∡C
A
Which angle is between the sides?
B
C
∡A
∡B
∡C
A
SAS
?
SSS
?
For ASA, two angles are congruent and the
side in between
For ASA, two angles are congruent and the
side in between
For ASA, two angles are congruent and the
side in between
For ASA, two angles are congruent and the
These angles are equal
side in between
For ASA, two angles are congruent and the
side in between
For ASA, two angles are congruent and the
These angles are equal
side in between
For ASA, two angles are congruent and the
side in between
For ASA, two angles are congruent and the
These sides are equal
side in between
The side has to be
For ASA, two angles are congruent and the
side in between
The side has to be
For ASA, two angles are congruent and the
BETWEEN the angles
side in between
The side has to be
For ASA, two angles are congruent and the
BETWEEN the angles
side in between
The side has to be
For ASA, two angles are congruent and the
BETWEEN the angles
This side is between
the angles
side in between
The side has to be
For ASA, two angles are congruent and the
BETWEEN the angles
These sides are not
between the angles
side in between
The side has to be
For ASA, two angles are congruent and the
BETWEEN the angles
side in between
The side has to be
For ASA, two angles are congruent and the
BETWEEN the angles
This side is between 
the angles
side in between
The side has to be
For ASA, two angles are congruent and the
BETWEEN the angles
These sides are not
between the angles
side in between
Which side is between the angles?
B
C
AB
AC
BC
A
Which side is between the angles?
B
C
AB
AC
BC
A
For SAA, there are two angles congruent and one side
For SAA, there are two angles congruent and one side
but the side is NOT between the angles
For SAA, there are two angles congruent and one side
but the side is NOT between the angles
For SAA, there are two angles congruent and one side
but the side is NOT between the angles
For SAA, there are two angles congruent and one side
but the side is NOT between the angles
These two angles are equal
For SAA, there are two angles congruent and one side
but the side is NOT between the angles
For SAA, there are two angles congruent and one side
but the side is NOT between the angles
These angles are equal
For SAA, there are two angles congruent and one side
but the side is NOT between the angles
For SAA, there are two angles congruent and one side
These sides are equal
but the side is NOT between the angles
For SAA, there are two angles congruent and one side
but the side is NOT between the angles
For SAA, there are two angles congruent and one side
but the side is NOT between the angles
This side is NOT between the angles
For SAA, there are two angles congruent and one side
but the side is NOT between the angles
For SAA, there are two angles congruent and one side
but the side is NOT between the angles
This side is NOT between the angles
SAA
?
ASA
?
For HL, you HAVE to have a right triangle
For HL, you HAVE to have a right triangle
and the hypotenuse and legs are equal
For HL, you HAVE to have a right triangle
and the hypotenuse and legs are equal
For HL, you HAVE to have a right triangle
and the hypotenuse and legs are equal
These are right trianlges
For HL, you HAVE to have a right triangle
Each hypotenuse is equal
and the hypotenuse and legs are equal
For HL, you HAVE to have a right triangle
and the hypotenuse and legs are equal
For HL, you HAVE to have a right triangle
and the hypotenuse and legs are equal
For HL, you HAVE to have a right triangle
and the hypotenuse and legs are equal
And the legs are equal
SAS
?
HL
?
NC
?
SAA
?
SSS
?
ASA
?
NC
?
SAA
?
ASA
?
SSS
?
A
Are these triangles congruent?
Yes
No
C
B
X
Z
Y
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