Download Triangle Congruence

G.6
Proving
Triangles
Congruent
1
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2
Objective: Students will
be able to determine
triangle congruence.
EQ: What strategies do
you use when
determining triangle
congruence?
3
The Idea of Congruence
Two geometric figures with
exactly the same size and
shape.
F
B
A
C
E
D
4
Do you need all six ?
NO !
SSS
SAS
ASA
AAS
5
Side-Side-Side (SSS)
If the sides of one triangle are congruent to the sides of a
second triangle, then the triangles are congruent.
Side
Side
1. AB  DE
2. BC  EF
3. AC  DF
Side
ABC   DEF
The triangles
are congruent by
SSS.
6
Side-Angle-Side (SAS)
If two sides and the included angle of one triangle are
congruent to the two sides and the included angle of another
triangle, then the triangles are congruent.
included
angle
Side
Side
1. AB  DE
2. A   D
3. AC  DF
Angle
ABC   DEF
The triangles
are congruent by
SAS.
Angle-Side-Angle (ASA)
7
If two angles and the included side of one triangle are
congruent to the two angles and the included side of another
triangle, then the triangles are congruent.
included
side
1. A   D
2. AB  DE
3.  B   E
Angle
Side
Angle
ABC   DEF
The triangles
are congruent by
ASA.
Angle-Angle-Side (AAS)
8
If two angles and a non-included side of one triangle are
congruent to the corresponding angles and side of another
triangle, then the triangles are congruent.
Non-included
side
1. A   D
2.  B   E
3. BC  EF
Angle
Side
Angle
ABC   DEF
The triangles
are congruent by
AAS.
9
Name That Postulate
(when possible)
SAS
SSA
Not enough
info!
ASA
AAS
Vertical Angles,
Reflexive Sides and Angles
10
When two triangles touch, there may be
additional congruent parts.
Vertical Angles
Reflexive Side
side shared by two
triangles
11
Name That Postulate
(when possible)
Reflexive
Property
SAS
Vertical
Angles
AAS
Vertical
Angles
SAS
Reflexive
Property
SSA
Not enough
info!
12
Reflexive Sides and Angles
When two triangles overlap, there may be
additional congruent parts.
Reflexive Side
side shared by two
triangles
Reflexive Angle
angle shared by two
triangles
Let’s Practice
13
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.
For ASA:
B  D
For SAS:
AC  FE
For AAS:
A  F