Proving Triangles Congruent. Two geometric figures with exactly the same size and shape. The Idea of...
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Transcript of Proving Triangles Congruent. Two geometric figures with exactly the same size and shape. The Idea of...
Two geometric figures with exactly the same size and shape.
The Idea of a CongruenceThe Idea of a Congruence
A C
B
DE
F
How much do you How much do you need to know. . .need to know. . .
. . . about two triangles to prove that they are congruent?
In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.
Corresponding PartsCorresponding Parts
ABC DEF
B
A C
E
D
F
1. AB DE
2. BC EF
3. AC DF
4. A D
5. B E
6. C F
Side-Angle-Side (SAS)Side-Angle-Side (SAS)
1. AB DE
2. A D
3. AC DF
ABC DEF
B
A
C
E
D
F
included angle
Angle-Side-Angle-Side-AngleAngle (ASA) (ASA)
1. A D
2. AB DE
3. B E
ABC DEF
B
A
C
E
D
F
included side
Angle-Angle-Side (AAS)Angle-Angle-Side (AAS)
1. A D
2. B E
3. BC EF
ABC DEF
B
A
C
E
D
F
Non-included
side
Warning:Warning: No SSA Postulate No SSA Postulate
A C
B
D
E
F
NOT CONGRUENT
There is no such thing as an SSA
postulate!
Warning:Warning: No AAA Postulate No AAA Postulate
A C
B
D
E
F
There is no such thing as an AAA
postulate!
NOT CONGRUENT
The Congruence PostulatesThe Congruence Postulates
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
SSA correspondence
AAA correspondence
Name That PostulateName That Postulate(when possible)
SASASS
SASSAS
SASASS
Reflexive Property
Vertical Angles
Vertical Angles
Reflexive Property SSSS
AA
Let’s PracticeLet’s PracticeIndicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
For SAS:
B D
For AAS: A F
AC FE
HWHWIndicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
For SAS:
For AAS: