Maths Presentation

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MATHS PROJECT
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Presented By
Suraj Kumar
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Basic details about the Congruence of
Triangles
Lets Go
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Congruent Triangles
Two triangles are congruent if they are the same
size and shape.
They are Congruent
Click
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Congruence of Triangles
Side Angle Side Criteria
Angle Side Angle Criteria
Angle Angle Side Criteria
Side Side Side Criteria
Right angle Hypotenuse Side Criteria
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Side Angle Side
If two triangles have two sides and the included
angle of the one equal to the corresponding sides
and the included angle of the other , then the
triangles are congruent.
Proof for SAS
AB DE (Side)
??B ?E (Included Angle)
BC EF (Side)
? ?ABC ? ?DEF (SAS)
is congruent to
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Side Angle Side 2 sides included angle of one
triangle equal those of the other triangle
Proof for SAS
4cm
AB DE (Side)
60o
??B ?E (Included Angle)
6cm
BC EF (Side)
? ?ABC ? ?DEF (SAS)
4cm
60o
is congruent to
6cm
End of Slide
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Congruence of Triangles
Side Angle Side Criteria
Angle Side Angle Criteria
Angle Angle Side Criteria
Side Side Side Criteria
Right angle Hypotenuse Side Criteria
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Angle Side Angle
If two angles and the included side of one
triangle are equal to the corresponding two
angles and the included side of the other
triangle,then the two triangles are congruent.
Proof for ASA
?A
?D (Angle)
AC DF (Side)
D
?F (Angle)
?C
F
E
? ?ABC ? ?DEF (ASA)
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Angle Side Angle
2 angles included side of one triangle equal
those of the other triangle.
Proof for ASA
60o
4cm
?A
?D (Angle)
BC DF (Side)
62o
?F (Angle)
?C
60o
4cm
? ?ABC ? ?DEF (ASA)
62o
is congruent to
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Congruence of Triangles
Side Angle Side Criteria
Angle Side Angle Criteria
Angle Angle Side Criteria
Side Side Side Criteria
Right angle Hypotenuse Side Criteria
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Angle Angle Side
If two angles and any side of a triangle are
equal to the corresponding angles and side of
another triangle then the two triangles are
congruent.
Proof for AAS
?A ?D (Angle)
??B ?E (Angle)
AB DE (Side)
? ?ABC ? ?DEF (AAS)
Click
is congruent to
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Angle Angle Side 2 angles corresponding side of
one triangle equal those of the other triangle.
Proof for AAS
60o
?A ?D (Angle)
4cm
??B ?E (Angle)
62o
AB DE (Side)
? ?ABC ? ?DEF (AAS)
60o
4cm
62o
is congruent to
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Congruence of Triangles
Side Angle Side Criteria
Angle Side Angle Criteria
Angle Angle Side Criteria
Side Side Side Criteria
Right angle Hypotenuse Side Criteria
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Side Side Side
If the three sides of one triangle are equal to
the corresponding three sides of another triangle
then the two triangles are congruent.
Proof for SSS
AB DE (Side)
BC EF (Side)
AC DF (Side)
? ?ABC ? ?DEF (SSS)
Click
is congruent to
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Side Side Side The 3 sides of one triangle equal
the 3 sides of the other triangle.
Proof for SSS
6cm
AB DE (Side)
4cm
BC EF (Side)
7cm
AC DF (Side)
? ?ABC ? ?DEF (SSS)
6cm
4cm
is congruent to
7cm
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Congruence of Triangles
Side Angle Side Criteria
Angle Side Angle Criteria
Angle Angle Side Criteria
Side Side Side Criteria
Right angle Hypotenuse Side Criteria
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Right angle Hypotenuse Side
Two right angled triangles are congruent if one
side and the hypotenuse of the one are
respectively equal to the corresponding side and
the hypotenuse of the other.
Proof for RHS
?B ?E (Right-angle)
AC DF (Hypotenuse)
AB DE (Side)
? ?ABC ? ?DEF (RHS)
Click
is congruent to
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Right-angle Hypotenuse Side
The right-angle, hypotenuse corresponding side
of one triangle equal those of the other.
Proof for RHS
5cm
?B ?E (Right-angle)
4cm
AC DF (Hypotenuse)
AB DE (Side)
? ?ABC ? ?DEF (RHS)
5cm
4cm
is congruent to
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THE END