Download Triangle Congruence

Triangle Congruence
3 line segments
(dried spaghetti sticks – make three different sizes)
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Take 3 line segments
Make a triangle
Mark the vertices
Draw the triangle
Now make a different triangle with the same
three segments that is not congruent
3 line segments - SSS Congruency
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NOT POSSIBLE
The two triangles are congruent, therefore
SSS Congruency – If the sides of
one /\ are @ to the sides of
another /\ then the /\’s are @ .
2 line segments & an angle
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Take 2 line segments
Make an angle on the overhead
Mark the endpoints and vertex
Draw the triangle
Now make a different triangle with the
same 2 segments & a protractor to measure
the angle
2 line segments & an angle – SAS @
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NOT POSSIBLE
The two triangles are congruent, therefore
SAS Congruency – If 2 sides and the
included angle of one /\ are @ to 2
sides and the included angle of
another /\ then the /\’s are @ .
2 angles & a line segment
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Pick 2 angle measures
Draw the 2 angles using the one side
Mark the endpoints and vertices
Draw the triangle
Now make a different triangle with the
same 2 angles & the side
2 angles & a line segment – ASA @
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NOT POSSIBLE
The two triangles are congruent, therefore
ASA Congruency – If 2 angles and
the included side of one /\ are @ to 2
angles and the included side of
another /\ then the /\’s are @ .
Triangle Congruence Postulates
@
ASA @
SAS @
SSS
Other Possibilities? AAA
Can you make another
triangle with same
angles but not
congruent?
32
87
61
Other Possibilities? AAA
32
32
87
87
61
61
You can have 3 angles
congruent and the
sides proportional.
These are Similar
Triangles
Other Possibilities…AAS
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Theorem
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Lets do the proof
Other Possibilities? SSA
Angle = 30
Other Possibilities? SSA
30
Other Possibilities? SSA
Given one angle and 2 sides not including
30
This is not a triangle congruence theorem!!