CLASS 7

1
CLASS 7

• CONGRUENCY OF TRIANGLES
• MADE BY S. K. GIRI TGT(MATHS)
• K.V. MAU(U.P)
• Patna Region

2
Proving Triangles Congruent
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The Idea of a Congruence
Two geometric figures with exactly the same
size and shape.
4
How much do you need to know. . .
. . . about two triangles to
prove that they are congruent?
5
Corresponding Parts
In Lesson 4.2, you learned that if all six pairs
of corresponding parts (sides and angles) are
congruent, then the triangles are congruent.
?ABC ? ? DEF
6
Do you need all six ?
NO !
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Side-Side-Side (SSS)
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Side-Angle-Side (SAS)


B

E






F
A



C
D

1. AB ? DE
2. ?A ? ? D
3. AC ? DF

?ABC ? ? DEF
included angle
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Included Angle
The angle between two sides
? H
? G
? I
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Included Angle
Name the included angle YE and ES ES and
YS YS and YE
? E
? S
? Y
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Angle-Side-Angle (ASA)


B

E






F
A



C
D

1. ?A ? ? D
2. AB ? DE
3. ? B ? ? E

?ABC ? ? DEF
included side
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Included Side
The side between two angles
GI
GH
HI
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Included Side
Name the included angle ?Y and ?E ?E and
?S ?S and ?Y
YE
ES
SY
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Angle-Angle-Side (AAS)


B

E






F
A



C
D

1. ?A ? ? D
2. ? B ? ? E
3. BC ? EF

?ABC ? ? DEF
Non-included side
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Warning No SSA Postulate
There is no such thing as an SSA postulate!
E
B
F
A
C
D
NOT CONGRUENT
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Warning No AAA Postulate
There is no such thing as an AAA postulate!
E
B
A
C
F
D
NOT CONGRUENT
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The Congruence Postulates
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Name That Postulate
(when possible)
SAS
ASA
SSA
SSS
19
Name That Postulate
(when possible)
AAA
ASA
SSA
SAS
20
Name That Postulate
(when possible)
Vertical Angles
Reflexive Property
SAS
SAS
Reflexive Property
Vertical Angles
SSA
SAS
21
HW Name That Postulate
(when possible)
22
HW Name That Postulate
(when possible)
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Lets Practice
Indicate the additional information needed to
enable us to apply the specified congruence
postulate.
For ASA
?B ? ?D
For SAS
?A ? ?F
For AAS
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HW
Indicate the additional information needed to
enable us to apply the specified congruence
postulate.
For ASA
For SAS
For AAS
25
THANKS