Post on 17-Mar-2016
description
Proving Triangles Congruent
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 4.3, we 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 DE2. BC EF3. AC DF4. A D5. B E6. C F
Do you need Do you need all six ?all six ?
NO !
SSSSASASAAAS
Side-Side-Side (SSS)Side-Side-Side (SSS)
1. AB DE2. BC EF3. AC DF
ABC DEF
B
A
C
E
D
F
Side-Angle-Side (SAS)Side-Angle-Side (SAS)
1. AB DE2. A D3. AC DF
ABC DEF
B
A
C
E
D
F
included angle
The angle between two sidesIncluded AngleIncluded Angle
G I H
Name the included angle:
YE and ES ES and YS YS and YE
Included AngleIncluded Angle
SY
E
E S Y
Angle-Side-Angle-Side-AngleAngle (ASA) (ASA)
1. A D2. AB DE3. B E
ABC DEF
B
A
C
E
D
F
included
side
The side between two anglesIncluded SideIncluded Side
GI HI GH
Name the included side:
Y and E E and S S and Y
Included SideIncluded Side
SY
E
YEESSY
Angle-Angle-Side (AAS)Angle-Angle-Side (AAS)
1. A D2. B E3. 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
SASSAS ASAASA
SSSSSSSSASSA
(when possible)
Name That PostulateName That Postulate(when possible)
ASAASA
SASASS
AAAAAA
SSASSA
Name That PostulateName That Postulate(when possible)
SASASS
SASSAS
SASASS
Reflexive Property
Vertical Angles
Vertical Angles
Reflexive Property SSSS
AA
HW: Name That PostulateHW: Name That Postulate(when possible)
(when possible)HW: Name That PostulateHW: Name That Postulate
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:
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