Download 4.2 Triangle Congruence by SSS and SAS

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4.2 Triangle Congruence by SSS and SAS
Objective:
To prove two triangles congruent using the SSS and SAS Postulates
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Angle-Side-Angle Postulate
ASA
 If
two angles and the included side of
one triangle are congruent to two angles
and the included side of another
triangle, then the two triangles are
congruent.
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Side-Side-Side Postulate
SSS
 If
3 sides of one triangle are congruent (≅) to
3 sides of another triangle, then the triangles
are congruent (≅).
ABC  DEF
Notice the order in
which the congruency
statement is given
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1.Which other side do we know is
congruent? Why?
1.Which two triangles are congruent?
1.How do you know?
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Included Angles
and Sides
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Side-Angle-Side Postulate
SAS
 If
2 sides and the included angle of one triangle
are congruent (≅) to 2 sides and the included
angle of another triangle, then the 2 triangles are
congruent (≅) .
ABC  DEF
Notice the order in which the congruency statement is given
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Practice Name the triangle congruence postulate, if any, that you can use
to prove each pair of triangles congruent. Then, write a congruence statement.
1.
2.
3.
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Practice
From the information given, can you prove
AEB  CDB ?
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Tips
 Mark
any given information on your diagram.
 Look
to see if your triangles “share” parts. These
common parts are automatically one set of congruent
parts.
 If
not given all the pieces you need to prove the
triangles congruent, look to see what else you might
know about the diagram. (For example: vertical
angles, shared sides, etc.)
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Methods that DO NOT Prove
Triangles to be Congruent
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Methods that DO NOT Prove
Triangles to be Congruent