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Proving Triangles Congruent. F. B. A. C. E. D. The Idea of a Congruence. Two geometric figures with exactly the same size and shape. How much do you need to know. . . . . . about two triangles to prove that they are congruent?. - PowerPoint PPT Presentation
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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?
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
Do you need Do you need all six ?all six ?
NO !
SSSSASHL
ASAAAS
Side-Side-Side (SSS)Side-Side-Side (SSS)
1. AB DE
2. BC EF
3. AC DF
ABC DEF
C
B
A
E
D
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
The angle between two sides
Included 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
Hypotenuse Leg (HL)Hypotenuse Leg (HL)
1. AB DE
2. B E
3. AC DF
ABC DEF
B
A
C
E
D
F
right 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
The side between two angles
Included SideIncluded Side
GI HI GH
Name the included side:
Y and E
E and S
S and Y
Included SideIncluded Side
SY
E
YE
ES
SY
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 or ASS Postulate No SSA or ASS Postulate
A C
B
D
E
F
NOT CONGRUENT
There is no such thing as an SSA
or ASS 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
SAS
HL
ASA
AAS
SSA or ASS
AAA
Name That PostulateName That Postulate
SASSASASAASA
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
Name That PostulateName That Postulate(when possible)
Reflexive Property SSSSSS
none
SSSSAA
AAAAAA
(when possible)Name That PostulateName That Postulate
Vertical Angles
ASAASAReflexive Property SSSS
AA
SASASS
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
Try it!Try it!Indicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
For SAS:
For AAS:
N V
MK TU
M U
